Received June 4, 2020, accepted June 15, 2020, date of publication June 19, 2020, date of current version July 1, 2020.

Digital Object Identifier 10.1109/ACCESS.2020.3003682

High Bit-Depth Seismic Data Compression: A Novel Codec Under the Framework of HEVC

MILOŠ RADOSAVLJEVIĆ 1, (Member, IEEE), ZIXIANG XIONG 2, (Fellow, IEEE), LIGANG LU3, (Senior Member, IEEE), DETLEF HOHL3, AND DEJAN VUKOBRATOVIĆ 1, (Senior Member, IEEE) 1Department of Power, Electronics, and Communication Engineering, University of Novi Sad, 21000 Novi Sad, Serbia 2Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843, USA 3Shell International Exploration and Production Inc., Houston, TX 77082, USA Corresponding author: Miloš Radosavljević ([email protected]) The work of Milos˘ Radosavljević and Dejan Vukobratović was supported in part by the European Union’s Horizon 2020 Research and Innovation Project under Grant 856697. The work of Zixiang Xiong was supported by the NSF grant CCF-2007527.

ABSTRACT Motivated by the superior performance of High Efficiency Video Coding (HEVC), and driven by the rapid growth in data volume produced by seismic surveys, in this work we explore a 32 bits per pixel (b/p) extension of the HEVC codec for compression of seismic data. We propose to reassemble seismic slices in a format that corresponds to video signal and benefit from the coding gain achieved by HEVC inter mode, besides the possible advantages of the (still image) HEVC intra mode. To this end, we modify almost all components of the original HEVC codec to cater for high bit-depth coding of seismic data: Lagrange multiplier used in optimization of the coding parameters has been adapted to the new data statistics, core transform and quantization have been reimplemented to handle the increased bit-depth range, and modified adaptive binary arithmetic coder has been employed for efficient entropy coding. Even though the new codec after implementation of the proposed modifications goes beyond the standardized HEVC, it still maintains a generic HEVC structure, and it is developed under the general HEVC framework. Thus, we tailored a specific codec design which, when compared to the JPEG-XR and commercial wavelet-based codec, significantly improves the peak-signal-to-noise-ratio (PSNR) vs. compression ratio performance for 32 b/p seismic data. Depending on a configuration, PSNR gain goes from 3.39 dB up to 9.48 dB. Also, relying on the specific characteristics of seismic data, we proposed an optimized encoder that reduces encoding time by 67.17% for All-I configuration on trace image dataset, and 67.39% for All-I, 97.96% for P2-configuration and 98.64% for B-configuration on 3D wavefield dataset, with negligible coding performance losses.

INDEX TERMS High bit-depth seismic data compression, 3D volumetric seismic data, HEVC.

I. INTRODUCTION AND MOTIVATION order of a few tens of terabytes of raw data per day. As a With recent advances in oil & gas exploration, sophisti- data burden is expected to become even greater in the future cated high-density imaging methods have been used to cre- with plans of new seismic surveys, there is an apparent need ate high-definition images of a subsurface geology, enabling for efficient coding technique that will meet high quality and more accurate mapping of the geologic structures, but con- high compression ratio requirements for diverse seismic data sequently creating huge volumes of data (both 2D traces and applications. As a matter of fact, the benefit of using efficient 3D wavefields). Some seismic images can have as many as compression scheme within the seismic surveys is twofold: 16 million pixels in one dimension, and most of them are 1) significant reduction of overall storage size required for high bit-depth images with 32 b/p resolution to cover a wide seismic data, targeting at the same time the highest possible dynamic seismic range. Thus, the amount of data sets being reconstruction quality, and 2) significant cost and time sav- processed in just one seismic survey commonly exceed the ings across the workflow where seismic data is generated, transferred, saved, copied and used. The associate editor coordinating the review of this manuscript and This work contributes to the goal of finding such an effi- approving it for publication was Gulistan Raja . cient compression solution by proposing a novel scheme for

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 8, 2020 114443 M. Radosavljević et al.: High Bit-Depth Seismic Data Compression: A Novel Codec Under the Framework of HEVC

seismic data compression under the framework of HEVC [1]. Range (JPEG-XR) [4], or licensed commercial wavelet-based Driven by the need of compression of seismic data and by codec [5]. the high compression efficiency of HEVC, this work studies Lastly, we emphasized that without proposed changes to the application of a 32 b/p extension of the HEVC codec. the original codec, direct application of the HEVC in its The decision to give preference to the HEVC in this study standardized form is not possible. Due to its specific design comes from the fact that 3D seismic data can have highly adapted to standard consumer video applications, where cer- correlated individual slices, resembling video signal, which tain losses are tolerable, some of the original components makes them particularly suitable for HEVC inter mode appli- render a huge error when applied to extended bit-depth data cation, besides the possible advantages of the (still image) (even without quantization). In that sense, aforementioned HEVC intra mode application [2]. Such approach, to treat modifications are introduced to replace those critical codec 3D seismic data as a sequence of frames in order to obtain parts. To the best of our knowledge there is no similar work higher compression gains by utilizing motion-compensated in the field of the seismic data compression that uses the predictive codec, is opposed to still image coding approaches HEVC as a base codec setting. Also, known to authors, that are frequently used and advised to be utilized by other there is no codec on the market for 32 b/p seismic data that competing lossy compression techniques in related literature. exploits redundancy in all three dimensions for improved However, it is important to note that, by using intra coding performance. Therefore, this work presents an initial effort to mode, the resulting codec also can handle still image com- provide valuable insights of using one well established coding pression of 2D trace images, along with aforementioned 3D scheme, such as one given with HEVC, for the purpose of seismic data compression. seismic data compression. Moreover, the standardized version of HEVC accepts input data up to 16 b/p [3], and it is mainly developed to maintain A. RELATED WORK ON LOSSY SEISMIC DATA high compression ratios for the most common applications COMPRESSION of the standard consumer video. Since seismic data use up to Compression performance of traditional transform based 32 b/p, the HEVC can not be directly applied. It is also very methods is mainly affected by the transform’s ability to decor- important not to threshold seismic data prior to compression relate acquired data. In most cases, after decorrelation has since some sensitive information may be lost, and this is the been applied, in order to represent data in the most compact main reason why we are not able to directly use standardized way, the usual subsequent steps that follow transform are 16 b/p version of HEVC. Thus, we have modified almost all adaptation of a properly designed quantizer, e.g., uniform or core components of the original codec to propose a novel frequency-adjusted, and efficient entropy coding, e.g., arith- coding scheme for high bit-depth seismic data compression metic, Huffman, or run-length coding. Several approaches under the HEVC framework. While the block division and using those principles have been compared in [5] and [6]. block structure, as well as the prediction part of the proposed Among many transforms, wavelet based approaches have codec mainly remain the same, other parts were subjected played a dominant role in performing decorrelation of seismic to major changes in order to cater targeted 32 b/p input. data [7]–[9]. The popularity of the wavelet based coding Standardized HEVC’s transform has been replaced with the scheme could be found in its efficient data representation new lifting-based transform of flexible block sizes rang- in the transformed domain which easily allows compressed ing from 4 × 4 to 32 × 32 pixels. Quantization has been image manipulation, e.g., by utilizing straightforward quality replaced with a uniform quantization scheme with increased control scheme or progressive image decompression. One quantization parameter range. At the end, modified context such effective coding scheme, based on set partitioning in adaptive binary arithmetic coder (CABAC) with additionally hierarchical trees (SPIHT), was recently adopted to seismic improved throughput has been utilized for efficient entropy data in [10], and also partially adopted by methods in [5]. coding. Also, a new model for the Lagrange multiplier has However, traditional wavelet-based approaches may not be been used in Rate-Distortion (RD) optimization loop in order well suited to the highly oscillatory nature of seismic data to accommodate extended bit-depth range and to empower according to [5]. To alleviate this problem, and to get closer extended quantization parameter range (as necessitated by to higher compression ratios than those achieved by using 32 bit-depth). Even though the new codec after implemen- traditional wavelet basis, one can utilize wavelet packets or tation of the proposed modifications goes beyond the stan- adaptive local cosines as proposed in [5], [11]–[13]. Also, dardized HEVC, it still maintains a generic HEVC structure, hybrid of wavelet with either wavelet packet or local cosine and it is developed under the general HEVC framework. are presented in [14]. Although the cosine basis proved to be a In addition, by adapting the proposed codec to the specific suitable transform for oscillatory patterns [15], the lack of an attributes of the seismic data, we proposed optimized encoder efficient coding scheme, such as those used with wavelets, which significantly reduces encoding time with negligible has put these approaches slightly aside. In part, this dis- compression performance losses. Our results using the pro- advantage has been overcome by method in [16] and soon posed codec (in both inter and intra coding mode) signifi- after in [17]. Conceptually similar work based on sub-band cantly outperform the performance of codecs that are widely decomposition using different filter-banks and other related used in industry for seismic data, such as JPEG eXtended transform-based approaches can also be found in [18], [19].

114444 VOLUME 8, 2020 M. Radosavljević et al.: High Bit-Depth Seismic Data Compression: A Novel Codec Under the Framework of HEVC

Novel approaches that increasingly take into account the highly flexible quadtree structure, HEVC introduces different nature of the seismic data (e.g., seismic image geometry), and block types. At a high level, HEVC divides the image into a that are able to sparsely represent seismic data at the same grid of non-overlapping Coding Tree Blocks (CTB). A CTB time, have been widely studied in related literature. Among can be of size of 64 × 64, 32 × 32, or 16 × 16 pixels. Fur- many, we point to covariance based decorrelation method thermore, a CTB can be recursively split into multiple coding such as principal component analysis (which is also known blocks (CB). Supported CB sizes start from the same size as as Karhunen-Loève transform) [20], [21], generalized Radon CTB to as small as 8 × 8. To carry out various prediction transform [22], or work in [23] based on regularized nonsta- parameters, prediction block (PB) has been introduced. In the tionary autoregression, or locally adaptive wavelets [24], and standard, PB partitioning is related to the proper selection a broad family of wavelet-like functions named x-lets, such of the partition mode. Square, rectangular, and asymmetric as bandlets [25], seislets [26], brushlets [27], dreamlets [28], rectangular partition modes (PB shapes) are supported in etc. Such a wide range of new class of bases result in var- HEVC. Hence, a CB may consist of either one PB with the ious new signal decomposition (and compression) designs, same edge as the CB, two rectangular PBs, or four square although they have been based on similar principles of sparse PBs, and PB size cannot be smaller than 4 × 4. In order to representation and coding of seismic data. better utilize the transform in HEVC, transform block (TB) Lastly, a compression technology that has been in use has been used. A TB is still dependent on the CB, but starting for many years by the industry is the licensed commercial from the CB level as a root, it may be recursively divided wavelet based scheme proposed in [5], which allows easy into 4 smaller square blocks. Thus, a TB has its own quadtree quality and rate control. It outperforms many other seismic partitioning, where TB sizes go from 4 × 4 to 32 × 32, compression schemes available at the market. Another recent supporting only square transform. standard image coding scheme JPEG-XR [4], whose aim is In our research we have kept the complete block structure low-complexity compression of high dynamic range images, and associated syntax of HEVC. Thus, for more details on has been utilized by the industry to compress 1-D and 2-D block partitioning readers are referred to [30]. We assumed seismic data [29]. Although JPEG-XR cannot compress all that the given block structure is well suited for seismic 32 bits of an input image (up to 24 b/p lossless and up to images since they can have large uniform regions that can 32 b/p lossy), low complexity makes it a good candidate for be compressed by using higher block sizes, and yet contain commercial use, since it is friendly to heavy workloads and regions with a lot of details that can be compressed by using hardware with low configuration. However, it is only limited smaller block sizes, which in turn maintains the ability to to still image compression. retain important seismic features. Since block partitioning is not directly associated with the extended bit-depth range, II. METHODS AND PROPOSED SOLUTIONS or with the fact that seismic data have been used instead of In this work, in order to meet the ever-growing requirements natural video, there is no need to modify this part. However, arising from new high-density seismic surveys, as a start- we underwent additional experiments that aim to show per- ing point, we use the standardized and ubiquitous, industry formance when some limitations on a block size are intro- accepted HEVC solution. The general coding design and the duced (see Sec. III-C). In that way we can show the usefulness modifications that we have introduced in the new codec, of the standardized block partitioning scheme, or on the other in order to accommodate extended bit-depth range, are given side, if experiments show negligible performance changes, in the following subsections, including the motivation that we can choose to adjust the encoder according to those find- leads to our selected design. We also point out parts that we ings and to unburden the encoder of unnecessary calculations. believe have space for further development and improvement. As the subject of further research, block partitioning can be The given analysis has been observed from the encoder side, considered in the context of algorithmic complexity reduc- however conforming decoder has also been developed in our tion, e.g., by using assumption that collocated blocks at the study in order to obtain reconstructed data after compression. same position in consecutive seismic slices are highly corre- Before going into more details, we point out that some lated and most likely have very similar content, structurally codec’s components such as those given in Sec. II-A and and statistically, mainly due to the low motion characteristics Sec. II-B mainly remain unchanged and less modified than of seismic data. In such way, some optimization scheme other parts. However, those components are greatly utilized that will speed-up block partitioning based on the previous during encoder complexity optimization which is presented in decisions may be utilized at this part of the codec. However, Sec. III-C. In that sense, for clarity purpose, we also describe advanced complexity reduction is not part of this work. them in more detail.

A. BLOCK STRUCTURE B. INTRA AND INTER PREDICTION HEVC uses block-based approach, where each input image 1) INTRA PREDICTION [31] is divided into non-overlapping square blocks that are addi- Spatially neighboring reference samples that are located at tionally recursively divided into variable size blocks to form a the top and on the left side of a PB have been exploited to quadtree structure [30]. In order to support such improved and calculate prediction signal. In certain cases, when reference

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samples are not available, or when they cannot be recon- one (uni-directional prediction) or two (bi-directional pre- structed by repeating the previously available samples, nomi- diction) motion vectors depending on the frame type (P or nal average value for a given bit-depth has been used (e.g., B frames). In the latter case, average values or weighted 231 for a 32 b/p seismic data). In addition, HEVC allows prediction of the predicted signals have been used. 35 different intra prediction modes. It utilizes 33 angular The motion compensated prediction process starts with the modes, along with DC and planar modes to model smooth advance motion vector prediction (AMVP) scheme, where regions more precisely. Intra mode signaling, reference sam- the encoder has to choose the motion vector predictor among ple manipulation, intra prediction mode design, and mode multiple predictor candidates [35]. Spatial candidates, tem- derivation remains the same as in HEVC [31]. porally collocated candidate, or zero-MV candidate can be To avoid full RD optimization calculations, HEVC’s ref- added to the list of competitors. Only two competitors from erence software (HM) [32] implements a fast algorithm for the list are further passed to the RD optimization module, and intra mode selection [33]. In the first stage, it calculates based on the minimal cost, one MV candidate is selected as a the N best prediction mode candidates using the sum of predictor for the particular PB. Later on, this predictor is used absolute Hadamard transform coefficients as the distortion as a starting point in ME. Although temporal candidates can measure DHad , which is a simplified version of the brute force be useful to improve performance, they require a significant approach. For the rate Rmode, it uses the number of bits nec- amount of the memory to store the motion-related data. Thus, essary to code a specific prediction mode only. The Lagrange we have tested the usefulness of the temporal predictor on the cost is then calculated as J = DHad + λRmode. More about seismic data compression performance. Lagrange cost and RD optimization can be found in Sec. II- Thereafter, ME continues by applying integer-sample pre- G. Thereafter, in the simplified J encoder, HEVC considers cision motion search. In our initial setup, full search is per- N best prediction modes for full RD optimization, where N formed in a predefined search window range, meaning that is [9, 9, 4, 4, 5] for block size [4 × 4, 8 × 8, 16 × 16, 32 × 32, each integer point displacement within the window has been 64 × 64], respectively. However, the optimal numbers for the checked in RD sense. One point, which has proved to be N candidates are provided based on experimental observa- the best in terms of the coding price, is selected for fur- tions by using natural video. In addition, those simplifications ther search. Fractional-sample ME is performed afterwards negatively affect the performance, which for natural video has within the neighborhood of the selected integer point. Eight been shown to be negligible. For seismic data, implications surrounding points are first evaluated using half-sample pre- of the simplified J encoder have not been analyzed yet, and cision, followed by eight quarter-sample search to fine tune further investigation must be conducted during development previously selected point. Finally, efficient coding of the pre- of the seismic data codec. Thus, at first we also start with diction information is utilized, where the difference between some limited number of modes for full RD optimization, and the MV predictor and the actual MV, and the index of the subsequently, we gradually increase and decrease this number AMVP candidate, are encoded into the bitstream. until some meaningful effect on performance is observed (see Similar MV prediction scheme as AMVP has been also Sec. III-C). In that way, after experiments on the optimal N used in MERGE and SKIP mode (special case of MERGE candidates are conducted, we were able to pick a suitable mode when no residual data is present in the bitstream), number of modes for full RD optimization that does not see [36] for more details on MERGE and SKIP mode in influence overall performance on seismic data. HEVC. Based on the set of the possible candidates, encoder In addition, the intra coding complexity still remains high may choose inter-coded PUs that share the same prediction and further computational savings are possible. We believe information, and hence it does not have to explicitly transmit that 33 angular modes are more than enough since seismic any motion information. The same candidates as in AMVP data do not possess as many textural structures as natural have been used, except at most five are selected for the full images do. This motivates us to focus our future research RD optimization. The number of competitors in MERGE to reduce the number of angular modes for fast encoding mode is controlled by the configurable parameter, and we without significant performance loss. In order to experiment vary it between 1 and 5 to show its influence on performance. with reduced number of intra modes, one simple option is In this work, by taking into account low-motion to utilize its the most frequent subset, as it is analyzed in characteristics of seismic data, we attempt to limit the Section III-C. search window range to the lowest possible while main- taining approximately the same coding performance. In 2) INTER PREDICTION [34] addition, instead of performing RD optimization on each Successive frames, or equivalently seismic slices, usually integer point within the window, we explore how test zone share structurally and statistically highly correlated regions. search (TZSearch) performs with seismic data. TZSearch To eliminate redundancy between slices, the encoder incor- combines diamond search, raster search, and star refinement porates prediction mechanism that is based on motion esti- methods to speed-up encoder with negligible loss in perfor- mation (ME). It consists of finding a displaced block within mance by omitting some integer-precision points in the RD a reference frame, where displacement is defined with motion optimization. A flow-chart of TZSearch algorithm can be vector (MV). In addition, each PB has been associated with found in [37]. Also, in this work, we examine the potential

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effectiveness of the half- and quarter-sample prediction when suitable for practical usage. For that reason, even though the applied to the seismic data. best energy compaction can be achieved when compared to other more practical solutions, floating-point DCT has been C. CORE TRANSFORM used mainly for comparison purpose in order to show the To obtain transformed coefficients, for each residual block, performance in terms of achievable coding gain and compu- two-dimensional (2D) transform with the same size as the tational speed, e.g., to estimate binDCT’s performance. TB has been used. Possible transform block sizes are ranging from 4 × 4 to 32 × 32 pixels. Only the Discrete Cosine 2) BinDCT Transform (DCT) [38], has been examined in our research. By utilizing the symmetry (and anti-symmetry) properties of Additionally, the DCT used in HEVC is an integer approx- the basis vectors, the number of arithmetic operations can be imation of the orthonormal (original floating-point) DCT. significantly reduced. For example, it could be achieved by Transform matrix coefficients are derived by approximat- using Chen’s factorization of the DCT matrices [39], which ing scaled DCT basis functions. The scaling factor used in consists of alternating cosine and sine butterfly matrices with 6+ M HEVC is 2 2 compared to an orthonormal DCT, where a binary butterfly matrices. In general, Chen’s algorithm may = n ≥ M = log2(N), and N is TB size. Also, to preserve the be used for any value of N 2 , where n 2, in contrast norm compared with orthonormal DCT and to keep dynamic to some other methods that are more efficient in terms of range within 15 bits without sign bit (as defined by standard), number or computational steps, but can not be generalized to additional scaling has been defined. A total scaling at the the arbitrary transform sizes. It turns out to be very important forward pass of the standardized DCT is 2(15−B−M), and total property due to the HEVC’s variable block size. That is scaling at the inverse transform is 2−(15−B−M). This scaling the main reason why we have decided to use the Chen’s is forwarded to the HEVC’s quantizer (see the following approach for a fast DCT implementation. For more detailed subsection), to simplify and reduce the calculations by jointly and systematic way of how to decompose a DCT matrix of an observing the transform scaled factors with the quantization arbitrary size, readers are referred to [39]. scaling. For more details about standardized DCT see [38]. Regardless, both aforementioned approaches still use Contrary to the orthogonal basis vectors, standardized floating-point multiplications, no matter if decomposition HEVC’s integer transform introduces losses, even when is done or not. In order to propose more practical solu- observed without the intermediate scaling, and quantization tion, we have examined a lifting-based scheme called the and dequantization steps. Thus, standardized transform is not binDCT [40]. We extend the idea of [40] and implement unitary, and it does not support perfect reconstruction either. binDCT of sizes 4 × 4, 8 × 8, 16 × 16, and 32 × 32, with This property shall play an important role in the design of the lifting steps derived by using already mentioned Chen’s our custom codec. Although it can be used for standard video factorization. Chen’s relationships with the binDCT scheme data, the approximate error will be magnified several orders comes from the point that each (non-binary) butterfly step can of magnitude for 32 b/p data, rendering it useless even without be additionally decomposed into three lifting steps. However, quantization. Also, HEVC adopts a better approximation of lifting coefficients are still floating points. Further approxi- 14+ M the DCT for 16 b/p data, with a scaling factor of 2 2 for mation is applied in order to permit fast multiplierless approx- forward transform (inverse transform kept the same scaling imations. Thus, binDCT is implemented by using lifting steps as before), and the maximum transform range that is limited with only binary shifts and additions, and floating-point lift- / m to 22 bits (without sign bit). However, the precision is still not ing coefficients approximated by dyadic values in k 2 form. good enough for 32 b/p data. Since many different implemen- Even with coefficients approximation with its dyadic values, tations of the DCT have been shown to be practically effective binDCT is lossless as long as forward and inverse transform in terms of the implementation cost and computational perfor- use the same shifting procedure. mance, we chose to keep using the DCT and re-implement it In order to enable different complexity vs. coding perfor- in order to empower extended bit-depth. mance trade-off, we have examined dyadic approximations with different accuracy. Depending on how we chose k/2m for 1) ORIGINAL FLOATING-POINT DCT different coefficients, we obtain different performances. Bet- As a straightforward solution, the original floating-point DCT ter approximation give us binDCT coefficients closer to the has been considered. It has been implemented by simple floating-point lifting coefficients, but requires more shifts and matrix multiplications. The transform matrix x is given with additions. However, due to large possible choices of approx- imations, it is important to determine dyadic lifting values r 2 (2j + 1)iπ  prior to implementation in order to avoid encoder-decoder x(i, j) = c(i) ∗ ∗ cos N 2N mismatch. After extensive experiments, in order to limit i = 0, 1,..., N − 1; j = 0, 1,..., N − 1 (1) complexity, and at the same time to closely approximate m √ floating-point values, we choose 2 = 32 as the highest where c(i) = 1/ 2 for i = 0, c(i) = 1 for i = 1, 2,..., N −1. allowed divisor in our setup (thus the highest shift is m = 5). However, floating-point multiplications are computation- Note that after Chen’s factorization, in total, 38 unique ally very intense in both software and hardware, and hence not floating-point lifting coefficients have to be calculated,

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distributed among 10 lifting stages (for the largest 32-point decoded level by the Qstep. Therefore, direct quantization binDCT). However, taking into account previous constraint after omitting HEVC’s integer approximation may be written (2m = 32) some of unique floating-point coefficients can be as fitted with the same dyadic value, leading us to only 18 unique coeff = ∗ −(15−M−B) + . . level 0 2 0 5 (5) lifting coefficient approximations, which also relax memory Qstep(Q ) requirements. It will be shown that selected design closely −(15−M−B) approximate original floating-point DCT, with significantly Downscaling by 2 is exactly the same as the lower computational complexity (see Sec. III-C). For more total upscale factor that has been introduced in the forward details on a selected dyadic values, see our binDCT imple- transform (necessary to preserve the norm of the original mentation at [41]. floating-point DCT and at the same time to have integer representation). Offset has been implied to secure rounding. D. QUANTIZATON Similarly, after redeployment for dequantization we can get 0 (15−M−B) The resulting coefficients after transform are subjected to the coeff = level ∗ Qstep(Q ) ∗ 2 + 0.5. (6) quantization process in order to further reduce the dynamic Q range and to get the quantized level. HEVC initially sup- Obviously, to extend the p range of the HEVC’s quan- tizer is straightforward, after which quantizer in (3) is wide ports quantization parameter Qp ranging from 0 to 51. For high bit-depth data, the given Q range is too narrow. Thus, enough to facilitate extended bit-depth range, e.g., maximum p Q ∼ 32 an additional offset is introduced to enable bit-depths higher step 2 . Thus, one solution is to use wrapped out than 8 b/p, leading to formulas given in (5) and in (6), however without any scaling factors, and in such way to use direct division/multiplication 0 Q = Qp + 6(B − 8), (2) with the quantization step size. Although this is the most logical solution, note that the quantizer in that way uses where B is the bit-depth, Q the input parameter, and Q0 p floating-point division/multiplication, which may be expen- is the new internal quantization parameter used by the sive and time consuming in both hardware and software. encoder/decoder. Taking offset into account, Q value can p In order to propose the more efficient solution, we com- be negative number, enabling lower compression ratio for pletely omit the HEVC’s quantizer, and make the most out of extended bit-depths. In the proposed seismic encoder, it could the uniform scalar quantizer proposed in [4]. We thus adapt be straightforward to extend the range of the quantization the quantizer mapping in which quantization parameter Q is parameter by simply setting B = 32 in (2). In such case, Q p p mapped to the scaling factors according to is in the range from -144 to 51, and consequently internal 0  , quantization parameter Q goes from 0 to 195. 1 Qp = 0 In HEVC, Q0 is not directly used for quantization, rather  Qstep = 2 ∗ Qp Qp < 16, (7) it is mapped to Q . Q is the actual uniform quantization step step man ∗ 2exp Q ≥ 16, step size, which is utilized in the quantization (and dequanti- P zation), and it is given as where man = 16 + (Qp%16) and exp = round(Qp/16). 0 In our codec, Qp ranges from 0 to 400 (MAX_QP = 400) 0 Q −4 ( 6 ). Qstep(Q ) = 2 (3) with Qp = 0 leading to lossless compression (assuming DCT transforms with perfect reconstruction). Also, limiting the The quantizer given in (3) can be also expressed as highest Qp to 400 is enough to facilitate high-dynamic range 0 29 0 Q since the maximum Qstep size is approximately 2 , which Qstep(Q ) = GQ0%6  round( ), (4) 6 is effectively more than enough for any practical purpose. and thereafter integer approximation of it is used by shifting Note that the new quantizer has a harmonic scale because −4/6 −3/6 −2/6 −1/6 0/6 1/6 and rounding values in G = [2 2 2 2 2 2 ] Qstep increases linearly with respect to Qp initially but grows to certain level to avoid direct division/multiplication at the exponentially later to allow high compression ratios for quantizer/dequantizer. Operator ‘’ represents bitshift, and high bit-depth images. This leads to fast implementation by ‘%’ is modulo operator. Thus, it can be implemented with bit-shifts (together with a few multiplications due to limited integer multipliers and shift operations only. More details number of ‘‘mantissas’’). Additionally, when compared with about integer quantizer implementation can be found in [38]. quantizer mapping in (3) that uses 195 different values to However, when incorporated in our codec, with adjusted approach maximum quantization step (∼ 232), the proposed DCT, the original HEVC’s integer approach cannot be quantizer mapping uses much finer scale to approach even anymore exploited, and it should be changed accordingly. lower quantization step (∼ 229). Thus, it leads to the quantizer Instead of using integer approximation of HEVC’s quan- step spacing that is sufficient enough to offer a wide range of tizer/dequantizer, one solution could be to directly utilize different qualities and rates. Qstep given with (3) (or equivalently with (4)). In such case, quantization is nothing more than division of the trans- E. ENTROPY CODING form coefficient (coeff) with the Qstep on the encoder side, HEVC utilizes Context Adaptive Binary Arithmetic and dequantization is equivalent to the multiplication of the Coder (CABAC) as the main entropy coding engine [42].

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It consists of three stages: syntax element binarization, con- – coeff_abs_level_remaining (remLevel) indicates remain- text modeling or bypass mode, and binary arithmetic coding. ing absolute quantized level. Binarization has been used to rewrite integer syntax ele- The given coding scheme in HEVC has been designed with ments, e.g., quantized levels, into binary codewords. In order the assumption that many quantized levels are zero or near to form a final bitstream, binary code is further compressed zero. Also, since gr1 and gr2 flags are coded in regular mode, by the arithmetic coder (AC). More precisely, moduo coder HEVC uses a mechanism to increase throughput by limiting (M-coder), a fast table-driven approximation of AC, is uti- the number of occurrence of those two flags within the one lized in HEVC [43]. The use of the standardized HEVC’s sub-block (SB), smaller non-overlapping 4 × 4 processing M-coder significantly reduces the coding complexity given units within TB, to 8 for gr1 and to 1 for gr2. However, the extensive use of multiplication operations during the considering high bit-depth extension, it is less likely to expect encoding process in the original form of the AC. Since occurrence of the low level coefficients, even at high fre- use of the given entropy coder has justification in the effi- quencies, and hence there is no benefit of using the original cient implementation, we have kept this part of the HEVC scheme. Instead, we further choose not to code the gr1 and as it is. gr2 flags. We completely cut-off those regularly coded bins In addition, AC can work in two modes - bypass or context in order to additionally improve the throughput by pushing adaptive mode (regular mode). In regular mode, different more bits to be coded in bypass mode. The proposed approach probability models (context models) have been assigned. reduces the number of context models, which in addition Context models have been initialized with a given pre-defined lowers the memory requirements, and it reduces the number probability distribution prior to coding. Initialization is Qp of bins coded in the regular mode, which in turn reduces dependent, and it is designed based on the extensive offline complexity. At the same time, performance has not been analysis of data statistics after quantization. However, in our affected by the proposed simplification. code it is configured such that the same initialization has been used for any Qp. We have kept the initialization of 2) BINARIZATION OF REMAINING ABSOLUTE LEVEL context models as HEVC’s initialization when Qp = 0, since In the standard, the remaining absolute level is defined as it most closely matches the data statistics that we expect in remLevel = level − (sigf + gr1 + gr2), where sigf our use-case (larger absolute levels of quantized coefficients). represents syntax element that indicates significance of the Similar approach has been used in the original HEVC design individual levels, e.g., whether it is zero or non-zero. How- for 16 b/p extension where all negative Qp values are clipped ever, we code all significant levels as remLevel = level − 1, to 0 prior to context initialization. Clearly, initialization of without exception, given the proposed changes with gr1 the context models might be sub-optimal for the seismic data and gr2 syntax elements. Due to large number of the bins statistics. Therefore, there is space to further explore a more that are required to code the quantized levels, all bins that efficient probability distribution for different Qp. Also, regu- emerged from remLevel are coded in bypass mode to improve lar mode in CABAC is highly sequential, given the nature of throughput. context modeling and data dependencies within it. Contrary To perform binarization of remLevel, HEVC originally to the regular mode, the bypass mode is used in order to speed uses adaptive process of Rice parameter initialization to up the whole encoding process and to improve throughput by control binarization, and combined Golomb-Rice (GR) assuming equal probabilities for both bin values (0 and 1). and k-th order Exponential-Golomb (EGk) binarization Since the increased bit-depth range changes no other syn- scheme [44], [45]. GR codes are used for smaller values of tax elements than the quantized level, we choose to exploit the remLevel, and switching to EGk is done when unary part (pre- most out of the HEVC’s coding engine, and to keep the most fix) of a GR code reaches 4. Then, the suffix is coded by parts related with syntax modeling, binarization, and syntax using the EGk codes, where k = r + 1, and r is Rice element coding. At the same time, the encoding of quantized parameter. levels involves several key elements that we completely inher- By using a given codes, codeword construction is not ited from the original HEVC, such as multi-level significance straightforward, and it depends on a tunable parameter r. For map coding, last significant level coding, sign coding, etc. each SB, r is initialized with rinit = 0, and updated as follows Those parts are left-out of the discussion, and more details ( r can be found in [42], [44], [45]. min(rmax , rcurrent + 1), remLevel > 3 ∗ 2 current rnext = rcurrent , otherwise, (8) 1) CODING OF THE ABSOLUTE QUANTIZED LEVEL To code absolute quantized level, HEVC utilizes syntax ele- with the cap at rmax = 4. Thus, depending on the previously ments such as: coded remLevel, r is either increased or kept constant, and – coeff_abs_level_greater1_flag (gr1) indicates whether it cannot be decreased inside the same SB. Due to extended the absolute coefficient amplitude is larger than one. range of absolute levels, aforementioned cap was omitted in – coeff_abs_level_greater2_flag (gr2) indicates whether order to better adapt binarization scheme to higher dynamic the absolute coefficient amplitude is larger than two. range. Also, for each SB, initialization has been changed in

VOLUME 8, 2020 114449 M. Radosavljević et al.: High Bit-Depth Seismic Data Compression: A Novel Codec Under the Framework of HEVC

a way that r at the beginning of the SB is not necessarily set F. ADDITIONAL CODING FEATURES to 0. Rather it is given with HEVC utilize several other (non-mandatory) coding features, c that we have decided to completely eliminate from our codec. r = round( ) The reason behind is that either they are insufficient for init 4  / our use-case or they introduce additional complexity at the c + 1, remLevel ≥ 3 ∗ 2round(c 4)  cost of insignificant coding gain. The excluded features are: round(c/4) cnext = c − 1, 2 ∗ remLevel < 2 ∧ c > 0 (9) Intra PCM, Transform Skip, Residual Rotation, Implicit and c, otherwise, Explicit Residual DPCM, Intra Reference Smoothing, Strong Intra Smoothing, In-loop Filtering, Adaptive Qp Selection, where c is set to 0 at the beginning of the CTB and updated and RD Optimized Quantization. The only feature utilized by accordingly once for each SB. However, it is updated in our codec is Sign Data Hiding (SDH) [44], which is based on the same way as before, which is given with (8), with an the approach where sign for the first non-zero coefficient in additional modification that removes the maximum value each SB does not have to be transmitted, but it can be inferred limitation entirely. Thus, the proposed adaptive binariza- based on the parity of the sum of the absolute coefficient tion scheme more efficiently adapts to the statistics of levels within SB. Since the sign bits can take up a substantial absolute quantized levels in the extended bit-depth range proportion of the compressed bitstream according to [44], scenario. based on detailed experiments we chose to adapt SDH and Also the EGk codes with limited prefix length have keep it as an essential feature in our codec, as consequence been used for a larger amplitudes. At the time when of the low computational complexity and improved overall GR code reaches 4 bins for the prefix part, switching coding gain. It is to note, SDH is lossy technique since it to the EGk code has to be performed, in which case changes the quantized level of the coefficients. Regardless, remLevel = level − 4 ∗ 2r − 1 has to be coded, and the this technique is optional, and we can chose to enable or resulting codeword is concatenated to the previously coded disable it by setting the flag at the encoder configuration, e.g., bins that emerged after GR binarization. By using the when full lossless reproduction is required. EGk binarization scheme, code length for remLevel has been kept within 32 bins. It has been achieved by limiting G. RATE-DISTORTION OPTIMIZATION - A NEW MODEL prefix bins based on the maximum dynamic range (after FOR THE LAGRANGE MULTIPLIER the DCT), which in HEVC is given with maxTrRange = To decide on an optimal coding parameter set, encoder deci- max(15, B + 6). Then, the prefix length is limited in the way sions are based on the RD optimization that use the method that maxPrefixExtensionLength = 28 − maxTrRange. When of Lagrangian multipliers [46]. In general, encoder tends to the maximum prefix length is reached, it is coded using trun- minimize cost J over the set of coding parameters, which is cated unary codes, and suffix is modified to accommodate given by J = D + λ ∗ R, where D is distortion measure, R the rest of the possible codes, maximizing its size. In that is rate, λ is the Lagrange multiplier which is applied to get way, the suffix length is given with exactly maxTrRange bins, the minimum RD cost, and parameter optimization has been and it is coded as fixed length representation. Obviously performed on each block of an image. the given scheme is not applicable in our codec since it The Lagrange multiplier directly controls the RD trade-off. cannot accommodate extended dynamic range after DCT. For example, small values of λ correspond to high bit-rates However, straightforward adjustment can make this approach and low distortion, while large values correspond to lower practically feasible to empower the use of 32 b/p data. First, bit-rates and higher distortion. More importance can be given maxTrRange = 37 since DCT proposed in our solution to D optimization or to R optimization by adjusting λ in the keeps the norm of the original DCT. Then we have modified cost function J. Therefore, the Lagrange multiplier plays a maximum prefix length as maxPrefixExtensionLength = crucial role in operational encoder control. 47 − maxTrRange, limiting prefix size to 10 bins. In HEVC, λ is calculated based on an RD model that is During our experiments, the selected prefix length has provided for natural images, and it is given by provided the best trade-off between performance and Qp−12 complexity. λ(Qp) = 0.57 ∗ 2 3 . (10) It can be shown that even with straightforward modifi- cations of CABAC our codec performs better than other With the proposed extended Qp range given in Sec. II-D, industry standards (see Sec. III-C). Thus, a foundation of for certain higher values of Qp, λ is also high which gives conceivable entropy coding scheme has been established, more importance to rate minimization without caring much lowering the complexity without compromising performance. about distortion loss. As a result, the encoder tends to choose A part that is related to the enhancement of the current scheme a parameter set that will reduce rate as much as possible. is left for future research, e.g., to improve the performance a In HEVC, the most rate conservative mode is the SKIP new binarization scheme and context initialization that would mode. By using the SKIP mode, the encoder may chose be specifically tailored for seismic data could be examined in to force residual block to be all zero since it is worth on future codec’s evolution. saving the number of the bits required to represent a given

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block, compared to the losses that are introduced in that way of λ. By using an extensive heuristic search, in this way we by truncating non-zero values, however with smaller overall were able to find the exact value of the new λ for each of the cost. Since λ can be high, it will enforce rate minimization newly extended Qp. In addition, using this approach requires and hence choose the SKIP mode much more often than it to store obtained λ for each Qp in the look-up table. is desirable. As a result of choosing SKIP without making To reach a solution that will not require look-up table, compromise in RD sense, a huge drop in performance is and thus relaxing memory requirements, we compare our detected for Qp values larger than 51, see Fig. 1a. It shows newly obtained λ value with previous ones given by (10). performance for the three consecutive frames of the same We propose to compensate the large values of λold when sequence (I frame and P frames that may be coded using Qp > 51 and hence provide better compromise between D SKIP mode), using the λ as it is defined in HEVC’s reference and R. We refer λ after we apply compensation as λnew, and Qp−a software. Naturally, P frames should have better performance we assume that it is still in the form of k ∗ 2 b (the same than I frames since better prediction may be achieved, which form as λold ). After observing newly proposed λ that are in our case is not observed due to λ non-optimality. From now stored in look-up table, we chose to have k = 2.1, a = −49, λ λ on we refer to given in (10) as old . and b = 8. It leads us to new recalculated λ that is given by

Qp+49 λnew(Qp) = 2.1 ∗ 2 8 . (11)

Fig. 1b shows the comparison between the λold and the λnew. It reveals a gap indicating that λold is very high compared with λnew (the gap is increasing with Qp) hence resulting in a low performance. However, as we are going to show, with the λnew we were able to improve coding performance. More importantly, by redefining the λnew, we made precise coding parameter allocation practically achievable. > λ FIGURE 1. (a) Example of performance drop after Qp 51 using old for the first three seismic slices of the same seismic sequence. (b) λ old III. EXPERIMENTAL SETUP AND RESULTS ANALYSIS compared with redefined λnew . A. DATA SET In order to achieve a good coding performance using our Our dataset is constructed from seismic data downloaded new codec, a critical consideration with regard to the optimal from publicly available sources, such as those listed at coding parameter selection is determination of the proper https://wiki.seg.org/index.php/Open_data. In our research we Lagrange multiplier λ. It is crucial to have proper λ for high use 20 real-field 2D trace images, and 10 synthetic 3D wave- range of Qp, in order to perform effective parameter allo- fields each having 30 slices. For example, in Fig. 2a we cation for the desired wide range of compression ratios and show one representative 2D trace image from our dataset. The reconstructed image qualities. Thus, we propose to redefine 808 × 3000 trace image (with 808 traces, 3000 samples per HEVC’s Lagrange multiplier in order to empower the use of trace) corresponds to the Alaska 2D survey, line 31-81 data. extended bit-depth and quantization parameter range in our 3D wavefield dataset is composed of samples of the forward new codec (as necessitated by 32 bit-depth extension). waveform propagation process generated by using a synthetic In this paper we use a simple but effective heuristic velocity models and wave-equation methods (to simulate approach. Theoretically, λ can take values from 0 (highest wave propagation through the defined subsurface models). rate, lowest distortion) to ∞ (lowest rate, highest distortion). In that way, by using numerical modeling, we are also allowed However, to maintain the practical meaning of Lagrange opti- to record wavefields, also called snapshots. Each snapshot mization, suitable values for λmin and λmax , that will balance is represented by a 3D array, resembling video signal, e.g., D and R, have been found for those boundary points, where characterized by two spatial and one temporal dimensions. λmin corresponds to Qp = 0 and λmax corresponds to Qp = For the illustration purpose, two representative frames (which MAX_QP. We manually tuned them to λmin = 0.0356 and we also refer as time slices) from our 3D compression dataset 18 λmax = 1.702 ∗ 10 . Also, by using our previously proposed are presented in Fig. 2b and Fig. 2c. Note, the terms frame and extended Qp and quantizer mapping function, we decided to slice are used with the same meaning in this paper. limit MAX_QP to the value of 400. Thus, we were able to reduce the search range to λ ∈ (λmin, λmax ) for any other B. EXPERIMETAL SETUP Qp in between 0 and MAX_QP. Since, λ is monotonically Experiments have been conducted on Linux workstation increasing function of Qp, it stands that λ(Qp −1) ≤ λ(Qp) ≤ powered by two Xeon processors at 2.1GHz, running λ(Qp + 1), and thus the search range can be additionally 16 processes in parallel, and using 8.3.0 gcc com- reduced. In that way we were able to make it feasible to piler. The proposed codec has been implemented on top implement targets, with acceptable complexity and accept- of the HM15.0+RExt-8.1 version of HEVC’s reference able precision, that lead us to the solution for any other values software [32].

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under the constraints of the application (memory, processing time, low motion nature of seismic images, etc.). Contrary to what is usually advised for standard video, we have used simple yet effective strategy given the assumption that the correlation between seismic slices is stronger when their dis- tance is smaller (from a picture order point of view). There- fore, coding configurations are given with, but not limited to, the following setup (see Fig. 3 for illustration): – All-I: All seismic slices are encoded independently by using only intra prediction. This is equivalent to baseline still image coding approaches. – P1-configuration: In addition, P frames are allowed to be used. All seismic slices within a group of pictures (GOP) use I frame (first frame in a GOP) and the first preceding P slice as a reference. GOP size is set to 8, and period of I frames is set to 8 as well, hence each GOP will start with an I frame. – P2-configuration: Previous configuration is also com- pared with the configuration that only uses just one pre- FIGURE 2. Sample input images. (a) Trace data corresponding to Alaska vious P frame as a reference, without referencing to the 2D land line 31-81 data; (b) 576 × 560 sample image which is part of a beginning of a GOP, and without any additional periods of synthetic 3D wavefield; (c) The 2nd 576 × 560 synthetic slice. I frames. – P3-configuration: To test performance when using differ- ent number of previous adjacent slices as a reference, instead The average difference between two RD-curves, has to use only previous slice, we use two and three preceding been given in terms of Bjøntegaard delta PSNR measure slices for referencing, which depends on a current slice posi- (BD-PSNR), similarly as in [47], [48]. However, in com- tion within the bitstream. We chose even slices to use two and parison to standard BD-PSNR calculation, in our work, odd slices to use three preceding reference frames. Only first BD-PSNR performance corresponds to the average PSNR frame is I frame, and the rest of the sequence uses P frames, difference in dB for the same compression ratio (CR) points. and GOP size is set to 8. In our assessment, average BD-PSNR is calculated between – B-configuration: In this configuration some slices may CR of 5:1 up to 45:1. We do not measure the average have a reference slices in both directions, hence it uses B performance outside this range for three reasons: 1) our frames as well. GOP size is set to 4. assumptions is that lower compression ratios can be achieved with lossless techniques, acquiring perfect reconstruction, C. PERFORMANCE ANALYSIS hence producing better performance than presented lossy We conducted several experiments in order to evaluate perfor- techniques, 2) higher CR introduce notable losses in data, and mance of the proposed codec. We also tested coding parame- would not be of particular interest for the targeted application, ter configurations that are specifically adapted to the seismic and 3) by limiting range of the CR points used in BD-PSNR data. calculations, we make sure to avoid the use of extrapolations of the RD-curves outside the end points. Besides the average 1) TEST 1 - CODING CONFIGURATIONS BD-PSNR characterization of the objective performance, for We first show performance comparison between five differ- illustrative purpose, we also plot RD-curves, with additional ent coding configurations given in Sec. III-B. We investi- enlarged part around CR 10:1 since it currently represents gated how to adapt reference picture management in order typical compression ratio for the seismic data applications. to establish compromise between encoding efficiency and Relative time of execution of encoding process is used to encoding complexity. From Fig. 4a and Table 1, we see approximate the complexity of one configuration relative to that B-configuration shows the best performance, followed T −T the another, which is given with 1T = tested reference ∗100%. by the P-configurations, and afterwards by image-based Treference Negative values reflect the time reduction in the execution (All-I) configuration. Such performance is expected since of the tested approach. The same approach to roughly eval- many works for compressing natural videos have proved uate complexity performance has been used during HEVC this. However, valuable insights arise when complexity is development. included in the analysis. By observing presented results, By our assessment, BD-PSNR change of at least 0.2 dB, Fig. 4a and Table 1, we can see that different P configu- and computational complexity change of at least 5%, have rations show almost identical average coding performance. been considered as significant. At the same time, the encoding complexity changes dramat- Five coding configurations have been applied for final ically depending on the chosen configuration. We can con- testing. They have been chosen to maximize performance clude that the increased number of reference slices does not

114452 VOLUME 8, 2020 M. Radosavljević et al.: High Bit-Depth Seismic Data Compression: A Novel Codec Under the Framework of HEVC

FIGURE 3. Cyclic GOP structure for different types of coding configurations.

FIGURE 4. Average RD-curves for Test 1, Test 2, and Test 3. (a) performance of different configuration choices given in Section III-B; (b) floating-point vs. binDCT average performance for trace image dataset; (c) floating-point vs. binDCT average performance for 3D wavefield dataset; (d) final performance after Test 3 for trace dataset; (d) final performance after Test 3 for 3D wavefield dataset.

improve coding gain for low-motion 3D seismic data, which TABLE 1. Average BD-PSNR and complexity performance of different is different from what is established for natural video [49]. coding configurations, relative to the proposed B-configuration. Thus, using only one previous reference slice, as given with P2-configuration, is more than enough to maintain the best coding performance with the lowest computational com- plexity and the lowest memory requirements (in terms of the buffer size). For example, 39.4% less encoding time 2) TEST 2 - binDCT than B-configuration is required for P2, compared to only As expected, obtained results showed that binDCT gives 2.89% less complexity when P1-configuration is used, and slightly lower performance than the original floating-point 30.35% increase in complexity for the most demanding DCT. Figure 4b and Figure 4c summarize average P3-configuration. Note that All-I is the least demanding con- performance comparison of binDCT, for trace data and 3D figuration, however with the price paid in lower performance. wavefield data, respectively. For 3D wavefield sequences, Regarding to the above results, we stick with the All-I, average BD-PSNR loss of binDCT is 0.33 dB. Trace images P2-configuration, and B-configuration in the following tests showed lower coding gain drop, where observed BD-PSNR to support different performance-complexity tradeoffs and is 0.17 dB. At the same time the computational complexity different use-cases (e.g., image based coding over predictive savings are 21.3% on average, as compared to the original coding). DCT with floating-point multiplications. Since the binDCT

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TABLE 2. Average BD-PSNR and complexity performance for different We see, Table 2, that limited minimum TB size resulted in block partitioning choices. decreased coding efficiency. However, we note that trace images are more affected by the test limitation compared to 3D wavefields. Given the previous results, we can conclude that the codec is highly sensitive to TB partitioning con- straints, and that variable transform size contributes greatly to improving the performance of the codec. Guided by the previous experiments, we decided to adapt block partitioning, and to optimize encoder by continuing with the following coding choices: 1) maximum CB size is set to 32×32 instead to 64×64; 2) minimum CB size is set to 16 × 16 instead of 8 × 8; 3) only square PB partition modes have been used; 4) minimum and maximum TB size has been kept unchanged, as well as relative residual quadtree depth which is set to 3 (as default in HM). Thereafter, we analyze the accumulated coding efficiency loss vs. total encoder speed-up after adjusting the block partitioning suit- ably. Results are illustrated on Fig. 4d and Fig. 4e for trace and wavefield data, respectively. We observed that the pro- posed adaptations lead to substantially large speed-up gain, time savings are highly desirable and coding gain is still at which on average goes to 85.22% for P and B configurations, high level, we henceforth stick to binDCT in the sequel as a and 26.62% for All-I configuration (when compared to the necessary change towards the practical solution. previous binDCT test). At the same time, almost the same coding performance has been observed, with 0.15 dB drop in 3) TEST 3 - BLOCK SIZE PSNR for 3D predictive coding and only 0.05 dB drop for From Table 2 we can see that, when the maximum allowed All-I configuration. It is important to note that the further CB size has been reduced from 64 × 64 to 32 × 32 pixels, experiments and performance comparisons are provided on the negligible influence on performance has been observed, top of aforementioned configuration choices. for both 3D wavefied and trace image data. In addition, when the maximum CB size has been reduced to 16 × 16, 4) TEST 4 - INTRA MODES the coding efficiency drop (BD-PSNR) becomes significant. After we analyzed compressed bitstreams, we observed that Also, we investigated sensitivity of the proposed codec on the modes 0, 1, 10 and 26 (planar, DC, horizontal and vertical) are limited minimum CB size, while the maximum CB size has chosen more often, followed by those around the vertical and been kept at 64 × 64. When minimum CB size is increased horizontal directions. We observe the same pattern of mode to 16 × 16, the performance remains approximately the distribution for different Qp values. In such way, we choose same, see Table 2. Increasing minimum CB size further to to use the following 23 intra modes in total {0, 1, 2, 4, 6, 32 × 32 brings a notable drop in performance that is no longer 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 25, 26, 27, 28, 30, 32, negligible. 34}, which combines modes 0, 1, 10, and 26, than those close Thereafter, asymmetric prediction block partitioning has to the vertical and horizontal directions, and every second been disabled in order to measure its contribution to the over- mode in between. Additionally, for a benchmark purpose we all coding gain. In such case, the average coding efficiency is also conduct test when only the following 12 intra modes slightly affected by the imposed limitation. On top of that, have been used {0, 1, 6, 8, 10, 12, 14, 22, 24, 26, 28, 30}. remaining rectangular partition modes have been removed PSNR vs. compression ratio performance evaluation, Table 3 from the available codec’s block structure, which show and Figures 5a and 5b, indicate that the average PSNR loss negligible coding efficiency drop. Bottom part of Table 2 is almost negligible when 23 subsampled modes have been summarize the coding performance of such PB partitioning used, and distinctly higher PSNR drop has been observed limitations. We can see that significant computational time by using only 12 subsampled modes. We comment that the savings can be achieved when all rectangular partition modes modest speedup (1T ) is the result of already optimized (including asymmetric) are disabled, with very low coding intra coding loop that uses a simplified HEVC encoder (see gain drop. Sec. II-B). Even when the number of total modes is signifi- Furthermore, results show that restricting the maximum cantly reduced, the same number of modes is always utilized TB size to 16×16 leads to a significant coding efficiency loss. in much more demanding brute force (full RD) optimiza- We also evaluated performance when minimum TB size is set tion approach. Despite that, we chose to keep 23 modes in to 8 × 8 while keeping maximum transform size at 32 × 32, follow-up experiments since negligible performance loss has which also requires to set minimum CB to 16×16 (minimum been detected in such way. It is worthwhile to point out that CB size must be strictly greater than minimum TB size). we tried to use uniformly decimated version of the 35 modes

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TABLE 3. Average BD-PSNR and complexity performance for intra mode number of candidates (12 or 16) does not lead to changes modifications. in compression performance, however computing resources have increased significantly, see Table 3. We also can see that the use of only 4 modes for full RD optimization pro- vides optimal trade-off between computational savings when compared to the utilization of 8 modes, with at the same time negligible compression performance change. Reducing in addition N to 3, 2, or 1 shows significant performance loss that is no longer negligible. Thus, we propose to use N = 4 as an optimal number of intra modes for full RD optimization (together with 23 intra modes in total) which does not degrade compression performance.

5) TEST 5 - MOTION ESTIMATION ME is computationally the most time consuming part of the codec. However, by taking into account the low-motion activity of seismic data, we can unburden the encoder of unnecessary calculations. Table 4 report the performance dur- ing several stages of adjusting the motion estimation process in HEVC by taking every second and every third angular to the seismic data. mode, however results showed lower coding performance We started with the default search range within the 64-pixel when compared to the proposed subsampling scheme. neighbourhood in anchor version, and in addition, we bring Next, we investigate how to configure the optimal N can- down the search range to only 1-pixel neighbourhood. Also, didates for full RD optimization in the simplified HEVC the search range for bi-prediction ME refinement has been set encoder. It is to note, in our anchor version we use to 1. Thus, integer-precision MV search has been reduced sig- 8 intra modes in full RD optimization loop. In this test, nificantly without compromising compression performance. we vary N between the following set of values N ∈ In order to additionally reduce the number of integer- {16, 12, 8, 4, 3, 2, 1}. Performance is summarized in Table 3, precision points we use modified TZSearch. Since we already and Fig. 5c and Fig. 5d. Experiment reveals that increased narrow the search range to 1, TZSearch uses only diamond

FIGURE 5. Average plots for Test 4 and Test 5. (a) All 35 intra modes vs. reduce number of intra modes for trace dataset; (b) All 35 intra modes vs. reduce number of intra modes for 3D wavefield dataset; (c) Reduced modes for full RDO for trace dataset; (d) Reduced modes for full RDO for 3D wavefield dataset; (e) Search range set to 1-pixel neighbourhood and modified TZSearch performance; (f) Performance comparison when fractional ME is disabled.

VOLUME 8, 2020 114455 M. Radosavljević et al.: High Bit-Depth Seismic Data Compression: A Novel Codec Under the Framework of HEVC

TABLE 4. Performance comparison of the proposed modifications within Hadamard measure for fractional ME. Thus, we chose to fully motion estimation loop. exploit fractional ME, since the ability of the encoder to track motion vectors by going below integer pixel precision proves to be beneficial in order to maintain high performance for low-motion seismic data. Since temporal predictor within AMVP scheme requires considerable storage capacity for motion related data of the collocated slice, we have decided not to use it in our setup. Also, its impact on the improved codec’s performance is negligible. Lastly, the number of competitors in MERGE mode is adjusted according to the tests, where we vary the search without proceeding to raster search in a second stage. number of merge candidates between 1 and 5. After conduct- However, in the refinement stage, which is derived if the ing results of the tests we chose to set the number of merge distance obtained from the previous stage is not zero, addi- candidates to 2, which represents the best trade-off between tional points may be checked in the RD sense. Since in the coding performance and encoding complexity. star refinement the number of additional points is not known in advance (search is repeated until the best distance equals D. SUMMARY OF TEST 1 TO TEST 5 zero), we decided to prevent the use of this fine tuning step. The given results reveal some useful findings that helped us That led us to only 4 integer-precision points that have to to propose the optimized encoder according to the applica- be checked within RD optimization. In addition, TZSearch tion scope. Results also imply that the optimized encoder employs additional motion vector prediction (different than may find better tradeoffs between the coding efficiency and the one given with AMVP). It uses left, upper, upper right, computational complexity. The performance difference due median, and zero predictors. However, after conducting sev- to the proposed adjustments is plotted in Fig. 6. When linked eral experiments, we decided to allow the use of median together, the proposed optimized codec reduces complexity predictor and zero-MV predictor to compete for MV predic- by the 67.17% for All-I configuration on trace image dataset, tion. Temporal predictor and other spatial predictors are not and 67.39% for All-I, 97.96% for predictive P-configuration, used in our setup. Performance of modified search range and and 98.63% for B-configuration on 3D wavefield dataset. TZSearch is presented in Table 4 and Fig. 5e. Proposed modi- At the same time, BD-PSNR loss is 0.27 dB on trace fication leads to almost identical overall coding performance, data, and 0.49, 0.65, and 0.64 dB on 3D wavefield dataset introducing significant complexity reduction. for All-I, P- and B-configuration, respectively. The coding Thereafter, in this work we first disable quarter-precision performance is given relative to the initial non-optimized and afterwards we disable half-precision MV estimation in (anchor) codec, see Fig. 6. Lastly, we note that decoder order to quantify its contribution to the overall coding gain. computational performance is approximately the same for According to the experiments, we found out that low-motion all configurations on both datasets. On average it is 16.6% seismic data highly benefit from such fine MV tuning. There less than that of the anchor decoder implementation. This are lot of fine details in seismic images that can be bet- final set of tools and methods reflect the application needs ter captured by using fine motion search. On top of that, as envisioned by the industry (in terms of performance and seismic images are considered to posses low-motion activ- complexity). ities, meaning that, from slice to slice, there is very little movement, which sometimes cannot be precisely captured E. COMPARATIVE RESULTS WITH OTHER METHODS by integer motion vector displacements. Notable BD-PSNR Fig. 7 plots the PSNR vs. compression ratio performance drop has been observed when we disabled quarter-precision of the proposed codec with JPEG-XR. In addition, Fig. 8 estimation. When we removed half-sample precision from plots performance comparison of the wavelet-based codec for the consideration (on top of the excluded quarter-precision), one trace image (Alaska 31-81 line), and one 3D wavefield the loss in performance became much more evident. Bare sequence. Unfortunately, we have passed Shell’s contract in mind that higher losses are noticed for P-configuration period for the project and hence do not have a license to since B-configuration could compensate lack of fractional run the wavelet-based codec to generate results for the entire precision by using averaged motion predictions from both dataset. However, based on the available results, we can see directions. Also, if fractional MV estimation is completely that wavelet-based codec performs similarly as JPEG-XR excluded, computing resources are slightly lower, which in over the wide range of compression ratios, see Fig. 8. comparison to the performance losses that are quite pro- Thus, average performance comparable to the one obtained nounced does not bring equally proportional computational with JPEG-XR could be expected over the complete dataset saving. Even that interpolations used to obtain fractional sam- for the second codec as well. Therefore, compared to a ples introduce additional complexity, and additional points JPEG-XR, which performs on par with licensed commercial have to be checked in the RD sense, such a small time wavelet-based codec, our new codec significantly improves reduction is result of the simplified search process which uses the PSNR vs. compression ratio performance.

114456 VOLUME 8, 2020 M. Radosavljević et al.: High Bit-Depth Seismic Data Compression: A Novel Codec Under the Framework of HEVC

FIGURE 6. Average performance comparison between the anchor and the optimized codec after Test 5 over: (a) trace image dataset, and (b) 3D wavefield dataset.

FIGURE 7. Average PSNR vs. compression ratio performance of the proposed codec. JPEG-XR [4] is included for comparison. Figure (a) corresponds to trace dataset, and (b) to 3D wavefield dataset.

FIGURE 8. The licensed commercial codec based on [5] vs. JPEG-XR [4]; (a) trace image, and (b) 3D wavefield sequence.

For JPEG-XR (similar improvement in PSNR is expected The overall performance of the new proposed 32 b/p codec for the second codec) average BD-PSNR gain is 5.86 dB shows that the modified HEVC framework is suitable for for the trace dataset (All-I configuration). For the 3D wave- seismic data compression since it improves coding gain by a field dataset, performance improvement is 3.39 dB for All-I, large margin when compared to the benchmarked solutions. 7.15 dB for P2, and 9.48 dB gain in PSNR is observed We also gave the executable version of our codec to geologists for B configuration, on average. A particularly pronounced to evaluate the impact of lossy compression, e.g., uniform improvement in PSNR can be observed for inter based pre- quantization noise, on interpretation of seismic images. Since dictive configurations (P2 and B). our new codec is performing much better than the one

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reported in [5] that the geologists currently use, they rate our [13] W. Wu, Z. Yang, Q. Qin, and F. Hu, ‘‘Adaptive seismic data compres- codec’s performance as highly satisfactory. sion using wavelet packets,’’ in Proc. Int. Symp. Geosci. Remote Sens., Jul./Aug. 2006, pp. 787–789. [14] A. Z. Averbuch, V. A. Zheludev, M. Guttmann, and D. D. Kosloff, ‘‘LCT- IV. CONCLUSIONS AND FUTURE WORK wavelet based algorithms for data compression,’’ Int. J. Wavelets, Multires- olution Inf. Process., vol. 11, no. 5, Sep. 2013, Art. no. 1350032. The apparent need for the research in the field of the seismic [15] Y. Wang and R.-S. Wu, ‘‘Seismic data compression by an adaptive local data compression is obvious and constantly increasing. Thus, cosine/sine transform and its effects on migration,’’ Geophys. Prospecting, we have designed the new, custom tailored, codec for high vol. 48, no. 6, pp. 1009–1031, Nov. 2000. [16] L. C. Duval and T. Q. 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[38] M. Budagavi, A. Fuldseth, G. Bjontegaard, V. Sze, and M. Sadafale, 2016 IEEE International Conference on Pattern Recognition, and the Best ‘‘Core transform design in the high efficiency video coding (HEVC) Demo Paper Award at the 2018 IEEE International Conference on Mul- standard,’’ IEEE J. Sel. Topics Signal Process., vol. 7, no. 6, timedia and Expo. He has served as an Associate Editor for the IEEE pp. 1029–1041, Dec. 2013. TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, from 1999 to [39] W.-H. Chen, C. Smith, and S. Fralick, ‘‘A fast computational algorithm 2005, the IEEE TRANSACTIONS ON IMAGE PROCESSING, from 2002 to 2005, for the discrete cosine transform,’’ IEEE Trans. Commun., vol. 25, no. 9, the IEEE TRANSACTIONS ON SIGNAL PROCESSING, from 2002 to 2006, the IEEE pp. 1004–1009, Sep. 1977. TRANSACTIONS ON SYSTEMS,MAN, AND CYBERNETICS—PART B, from 2005 to [40] J. Liang and T. D. Tran, ‘‘Fast multiplierless approximations of the DCT 2009, and the IEEE TRANSACTIONS ON COMMUNICATIONS, from 2008 to 2013. with the lifting scheme,’’ IEEE Trans. Signal Process., vol. 49, no. 12, pp. 3032–3044, Dec. 2001. He is currently an Associate Editor of the IEEE TRANSACTIONS ON MULTIMEDIA. [41] Source Code: BinDCT. Accessed: Jun. 19, 2020. [Online]. Available: https://github.com/Sh0lim/BinDCT LIGANG LU (Senior Member, IEEE) is currently [42] V. Sze and M. Budagavi, ‘‘High throughput CABAC entropy coding with Shell International Exploration and Produc- in HEVC,’’ IEEE Trans. Circuits Syst. Video Technol., vol. 22, no. 12, tion Inc., leading projects in machine learning pp. 1778–1791, Dec. 2012. [43] A. Moffat, R. M. Neal, and I. H. Witten, ‘‘Arithmetic coding revisited,’’ for oil and gas exploration, well completion data ACM Trans. Inf. Syst., vol. 16, no. 3, pp. 256–294, Jul. 1998. analytics, and seismic data compression. Before [44] J. Sole, R. Joshi, N. Nguyen, T. Ji, M. Karczewicz, G. Clare, F. Henry, joining Shell, he worked at the IBM Watson and A. Duenas, ‘‘Transform coefficient coding in HEVC,’’ IEEE Trans. Research Center. He is also an Adjunct Profes- Circuits Syst. Video Technol., vol. 22, no. 12, pp. 1765–1777, Dec. 2012. sor with the Department of Electrical and Com- [45] T. Nguyen, P. Helle, M. Winken, B. Bross, D. Marpe, H. Schwarz, and puter Engineering, Texas A&M University. His T. Wiegand, ‘‘Transform coding techniques in HEVC,’’ IEEE J. Sel. Topics research interests include machine learning, data Signal Process., vol. 7, no. 6, pp. 978–989, Dec. 2013. analytics, high-performance computing, and signal processing. He holds [46] T. Wiegand and B. Girod, ‘‘Lagrange multiplier selection in hybrid video over 40 granted patents and authored or coauthored over 70 peer-reviewed coder control,’’ in Proc. Int. Conf. Image Process., vol. 3, Oct. 2001, technical articles. He has served as a Committee Member for the Oil and Gas pp. 542–545. High Performance Computing Conference, in 2016 and 2017. He was the [47] G. Bjontegarrd, Calculation of Average PSNR Differences Between RD- General Co-Chair of the International Conference in Visual Communication Curves, document VCEG-M33, 2001. and Image Processing (VCIP), in 2008, and the Chair of the IBM Research [48] G. Bjontegaard, Improvements of the BD-PSNR Model, VCEG-AI11, Stan- dard ITU-T Q. 6/SG16, 34th VCEG Meeting, Berlin, Germany, Jul. 2008. Signal Processing Professional Interest Community, in 2003 and 2004. [49] T. Wiegand, X. Zhang, and B. Girod, ‘‘Long-term memory motion- compensated prediction,’’ IEEE Trans. Circuits Syst. Video Technol., vol. 9, DETLEF HOHL received the master’s degree no. 1, pp. 70–84, Feb. 1999. in chemistry from the Technical University of Munich and the Ph.D. degree in theoretical physics from the Technical University of Aachen, Ger- many. Before joining Shell, he was a Senior Staff Member with the German National Laboratory, Forschungszentrum Jlich. He spent two years as a Postdoctoral Researcher with the National Center MILOŠ RADOSAVLJEVIĆ (Member, IEEE) is for Supercomputing Applications, University of currently pursuing the Ph.D. degree with the Illinois, and one year at Stanford University. He is Department of Power, Electronics, and Commu- currently the General Manager for Computation and Modeling in Shell nication Engineering, University of Novi Sad, Research. He is also an Adjunct Professor with Rice University (computa- Serbia. He is currently a Research Assistant with tional and applied mathematics). the Department of Power, Electronics, and Com- munication Engineering, University of Novi Sad. His main research interest includes video and DEJAN VUKOBRATOVIĆ (Senior Member, image compression. He is also interested in the IEEE) received the Dipl.-Ing., Mr.-Ing., and field of computer vision and deep neural networks. Dr.-Ing. degrees in electrical engineering from the University of Novi Sad, Serbia, in 2001, 2005, and 2008, respectively. Since February 2009, he has been an Assistant Professor with the Department of Power, Electronics and Communication Engi- neering, University of Novi Sad, where he has been an Associate Professor, since March 2014, ZIXIANG XIONG (Fellow, IEEE) received the and a Full Professor, since April 2019. From Ph.D. degree in electrical engineering from June 2009 to December 2010, he was on leave as a Marie Curie the University of Illinois at Urbana-Champaign, Intra-European Fellow (FP7-PEOPLE-2008-IEF Project MMSTREAM) in 1996. From 1995 to 1997, he was with Prince- with the Department of Electronic and Electrical Engineering, University of ton University, first as a Visiting Student, and Strathclyde, Glasgow, U.K. From 2011 to 2014, his research at the University then as a Research Associate. From 1997 to 1999, of Novi Sad is supported in part by the Marie Curie European Rein- he was with the University of Hawaii. Since 1999, tegration Grant (FP7-PEOPLE-2010-ERG Project MMCODESTREAM). he has been with the Department of Electrical and His research group was involved in the FP7-PEOPLE-2011-IRSES Project Computer Engineering, Texas A&M University, QoSTREAM, from 2012 to 2016, and the FP7-PEOPLE-2013-ITN Project where he is currently a Professor and the Associate ADVANTAGE, from 2014 to 2018. He is involved in the H2020-PEOPLE- Department Head. He spent his sabbatical leaves at Stanford University, 2015-RISE Project SENSIBLE, from 2017 to 2021, and the H2020- in spring 2010, and Monash University, Australia, from 2017 to 2018. WIDENING-2018-TWINNING Project INCOMING, from 2020 to 2022. He received the NSF Career Award, in 1999, the ARO Young Investigator His research interests include information theory and communications Award, in 2000, and the ONR Young Investigator Award, in 2001. He was theory, more precisely, in the area of sparse-graph codes and network a co-recipient of the 2006 IEEE Signal Processing Magazine Best Paper coding and applications of related ideas in wireless multimedia delivery and Award, the top 10% paper awards at the 2011 and 2015 IEEE Multimedia next-generation wireless mobile cellular networks. Signal Processing Workshops, the IBM Best Student Paper Award at the

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