A Study for Image Compression Using Re-Pair Text-Based Algorithm
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The Discrete Cosine Transform (DCT): Theory and Application
The Discrete Cosine Transform (DCT): 1 Theory and Application Syed Ali Khayam Department of Electrical & Computer Engineering Michigan State University March 10th 2003 1 This document is intended to be tutorial in nature. No prior knowledge of image processing concepts is assumed. Interested readers should follow the references for advanced material on DCT. ECE 802 – 602: Information Theory and Coding Seminar 1 – The Discrete Cosine Transform: Theory and Application 1. Introduction Transform coding constitutes an integral component of contemporary image/video processing applications. Transform coding relies on the premise that pixels in an image exhibit a certain level of correlation with their neighboring pixels. Similarly in a video transmission system, adjacent pixels in consecutive frames2 show very high correlation. Consequently, these correlations can be exploited to predict the value of a pixel from its respective neighbors. A transformation is, therefore, defined to map this spatial (correlated) data into transformed (uncorrelated) coefficients. Clearly, the transformation should utilize the fact that the information content of an individual pixel is relatively small i.e., to a large extent visual contribution of a pixel can be predicted using its neighbors. A typical image/video transmission system is outlined in Figure 1. The objective of the source encoder is to exploit the redundancies in image data to provide compression. In other words, the source encoder reduces the entropy, which in our case means decrease in the average number of bits required to represent the image. On the contrary, the channel encoder adds redundancy to the output of the source encoder in order to enhance the reliability of the transmission. -
Arithmetic Coding
Arithmetic Coding Arithmetic coding is the most efficient method to code symbols according to the probability of their occurrence. The average code length corresponds exactly to the possible minimum given by information theory. Deviations which are caused by the bit-resolution of binary code trees do not exist. In contrast to a binary Huffman code tree the arithmetic coding offers a clearly better compression rate. Its implementation is more complex on the other hand. In arithmetic coding, a message is encoded as a real number in an interval from one to zero. Arithmetic coding typically has a better compression ratio than Huffman coding, as it produces a single symbol rather than several separate codewords. Arithmetic coding differs from other forms of entropy encoding such as Huffman coding in that rather than separating the input into component symbols and replacing each with a code, arithmetic coding encodes the entire message into a single number, a fraction n where (0.0 ≤ n < 1.0) Arithmetic coding is a lossless coding technique. There are a few disadvantages of arithmetic coding. One is that the whole codeword must be received to start decoding the symbols, and if there is a corrupt bit in the codeword, the entire message could become corrupt. Another is that there is a limit to the precision of the number which can be encoded, thus limiting the number of symbols to encode within a codeword. There also exist many patents upon arithmetic coding, so the use of some of the algorithms also call upon royalty fees. Arithmetic coding is part of the JPEG data format. -
Information Theory Revision (Source)
ELEC3203 Digital Coding and Transmission – Overview & Information Theory S Chen Information Theory Revision (Source) {S(k)} {b i } • Digital source is defined by digital source source coding 1. Symbol set: S = {mi, 1 ≤ i ≤ q} symbols/s bits/s 2. Probability of occurring of mi: pi, 1 ≤ i ≤ q 3. Symbol rate: Rs [symbols/s] 4. Interdependency of {S(k)} • Information content of alphabet mi: I(mi) = − log2(pi) [bits] • Entropy: quantifies average information conveyed per symbol q – Memoryless sources: H = − pi · log2(pi) [bits/symbol] i=1 – 1st-order memory (1st-order Markov)P sources with transition probabilities pij q q q H = piHi = − pi pij · log2(pij) [bits/symbol] Xi=1 Xi=1 Xj=1 • Information rate: tells you how many bits/s information the source really needs to send out – Information rate R = Rs · H [bits/s] • Efficient source coding: get rate Rb as close as possible to information rate R – Memoryless source: apply entropy coding, such as Shannon-Fano and Huffman, and RLC if source is binary with most zeros – Generic sources with memory: remove redundancy first, then apply entropy coding to “residauls” 86 ELEC3203 Digital Coding and Transmission – Overview & Information Theory S Chen Practical Source Coding • Practical source coding is guided by information theory, with practical constraints, such as performance and processing complexity/delay trade off • When you come to practical source coding part, you can smile – as you should know everything • As we will learn, data rate is directly linked to required bandwidth, source coding is to encode source with a data rate as small as possible, i.e. -
Probability Interval Partitioning Entropy Codes Detlev Marpe, Senior Member, IEEE, Heiko Schwarz, and Thomas Wiegand, Senior Member, IEEE
SUBMITTED TO IEEE TRANSACTIONS ON INFORMATION THEORY 1 Probability Interval Partitioning Entropy Codes Detlev Marpe, Senior Member, IEEE, Heiko Schwarz, and Thomas Wiegand, Senior Member, IEEE Abstract—A novel approach to entropy coding is described that entropy coding while the assignment of codewords to symbols provides the coding efficiency and simple probability modeling is the actual entropy coding. For decades, two methods have capability of arithmetic coding at the complexity level of Huffman dominated practical entropy coding: Huffman coding that has coding. The key element of the proposed approach is given by a partitioning of the unit interval into a small set of been invented in 1952 [8] and arithmetic coding that goes back disjoint probability intervals for pipelining the coding process to initial ideas attributed to Shannon [7] and Elias [9] and along the probability estimates of binary random variables. for which first practical schemes have been published around According to this partitioning, an input sequence of discrete 1976 [10][11]. Both entropy coding methods are capable of source symbols with arbitrary alphabet sizes is mapped to a approximating the entropy limit (in a certain sense) [12]. sequence of binary symbols and each of the binary symbols is assigned to one particular probability interval. With each of the For a fixed probability mass function, Huffman codes are intervals being represented by a fixed probability, the probability relatively easy to construct. The most attractive property of interval partitioning entropy (PIPE) coding process is based on Huffman codes is that their implementation can be efficiently the design and application of simple variable-to-variable length realized by the use of variable-length code (VLC) tables. -
Fast Algorithm for PQ Data Compression Using Integer DTCWT and Entropy Encoding
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 22 (2017) pp. 12219-12227 © Research India Publications. http://www.ripublication.com Fast Algorithm for PQ Data Compression using Integer DTCWT and Entropy Encoding Prathibha Ekanthaiah 1 Associate Professor, Department of Electrical and Electronics Engineering, Sri Krishna Institute of Technology, No 29, Chimney hills Chikkabanavara post, Bangalore-560090, Karnataka, India. Orcid Id: 0000-0003-3031-7263 Dr.A.Manjunath 2 Principal, Sri Krishna Institute of Technology, No 29, Chimney hills Chikkabanavara post, Bangalore-560090, Karnataka, India. Orcid Id: 0000-0003-0794-8542 Dr. Cyril Prasanna Raj 3 Dean & Research Head, Department of Electronics and communication Engineering, MS Engineering college , Navarathna Agrahara, Sadahalli P.O., Off Bengaluru International Airport,Bengaluru - 562 110, Karnataka, India. Orcid Id: 0000-0002-9143-7755 Abstract metering infrastructures (smart metering), integration of distributed power generation, renewable energy resources and Smart meters are an integral part of smart grid which in storage units as well as high power quality and reliability [1]. addition to energy management also performs data By using smart metering Infrastructure sustains the management. Power Quality (PQ) data from smart meters bidirectional data transfer and also decrease in the need to be compressed for both storage and transmission environmental effects. With this resilience and reliability of process either through wired or wireless medium. In this power utility network can be improved effectively. Work paper, PQ data compression is carried out by encoding highlights the need of development and technology significant features captured from Dual Tree Complex encroachment in smart grid communications [2]. -
Block Transforms in Progressive Image Coding
This is page 1 Printer: Opaque this Blo ck Transforms in Progressive Image Co ding Trac D. Tran and Truong Q. Nguyen 1 Intro duction Blo ck transform co ding and subband co ding have b een two dominant techniques in existing image compression standards and implementations. Both metho ds actually exhibit many similarities: relying on a certain transform to convert the input image to a more decorrelated representation, then utilizing the same basic building blo cks such as bit allo cator, quantizer, and entropy co der to achieve compression. Blo ck transform co ders enjoyed success rst due to their low complexity in im- plementation and their reasonable p erformance. The most p opular blo ck transform co der leads to the current image compression standard JPEG [1] which utilizes the 8 8 Discrete Cosine Transform DCT at its transformation stage. At high bit rates 1 bpp and up, JPEG o ers almost visually lossless reconstruction image quality. However, when more compression is needed i.e., at lower bit rates, an- noying blo cking artifacts showup b ecause of two reasons: i the DCT bases are short, non-overlapp ed, and have discontinuities at the ends; ii JPEG pro cesses each image blo ck indep endently. So, inter-blo ck correlation has b een completely abandoned. The development of the lapp ed orthogonal transform [2] and its generalized ver- sion GenLOT [3, 4] helps solve the blo cking problem to a certain extent by b or- rowing pixels from the adjacent blo cks to pro duce the transform co ecients of the current blo ck. -
Video/Image Compression Technologies an Overview
Video/Image Compression Technologies An Overview Ahmad Ansari, Ph.D., Principal Member of Technical Staff SBC Technology Resources, Inc. 9505 Arboretum Blvd. Austin, TX 78759 (512) 372 - 5653 [email protected] May 15, 2001- A. C. Ansari 1 Video Compression, An Overview ■ Introduction – Impact of Digitization, Sampling and Quantization on Compression ■ Lossless Compression – Bit Plane Coding – Predictive Coding ■ Lossy Compression – Transform Coding (MPEG-X) – Vector Quantization (VQ) – Subband Coding (Wavelets) – Fractals – Model-Based Coding May 15, 2001- A. C. Ansari 2 Introduction ■ Digitization Impact – Generating Large number of bits; impacts storage and transmission » Image/video is correlated » Human Visual System has limitations ■ Types of Redundancies – Spatial - Correlation between neighboring pixel values – Spectral - Correlation between different color planes or spectral bands – Temporal - Correlation between different frames in a video sequence ■ Know Facts – Sampling » Higher sampling rate results in higher pixel-to-pixel correlation – Quantization » Increasing the number of quantization levels reduces pixel-to-pixel correlation May 15, 2001- A. C. Ansari 3 Lossless Compression May 15, 2001- A. C. Ansari 4 Lossless Compression ■ Lossless – Numerically identical to the original content on a pixel-by-pixel basis – Motion Compensation is not used ■ Applications – Medical Imaging – Contribution video applications ■ Techniques – Bit Plane Coding – Lossless Predictive Coding » DPCM, Huffman Coding of Differential Frames, Arithmetic Coding of Differential Frames May 15, 2001- A. C. Ansari 5 Lossless Compression ■ Bit Plane Coding – A video frame with NxN pixels and each pixel is encoded by “K” bits – Converts this frame into K x (NxN) binary frames and encode each binary frame independently. » Runlength Encoding, Gray Coding, Arithmetic coding Binary Frame #1 . -
Predictive and Transform Coding
Lecture 14: Predictive and Transform Coding Thinh Nguyen Oregon State University 1 Outline PCM (Pulse Code Modulation) DPCM (Differential Pulse Code Modulation) Transform coding JPEG 2 Digital Signal Representation Loss from A/D conversion Aliasing (worse than quantization loss) due to sampling Loss due to quantization Digital signals Analog signals Analog A/D converter signals Digital Signal D/A sampling quantization processing converter 3 Signal representation For perfect re-construction, sampling rate (Nyquist’s frequency) needs to be twice the maximum frequency of the signal. However, in practice, loss still occurs due to quantization. Finer quantization leads to less error at the expense of increased number of bits to represent signals. 4 Audio sampling Human hearing frequency range: 20 Hz to 20 Khz. Voice:50Hz to 2 KHz What is the sampling rate to avoid aliasing? (worse than losing information) Audio CD : 44100Hz 5 Audio quantization Sample precision – resolution of signal Quantization depends on the number of bits used. Voice quality: 8 bit quantization, 8000 Hz sampling rate. (64 kbps) CD quality: 16 bit quantization, 44100Hz (705.6 kbps for mono, 1.411 Mbps for stereo). 6 Pulse Code Modulation (PCM) The 2 step process of sampling and quantization is known as Pulse Code Modulation. Used in speech and CD recording. audio signals bits sampling quantization No compression, unlike MP3 7 DPCM (Differential Pulse Code Modulation) 8 DPCM (Differential Pulse Code Modulation) Simple example: Code the following value sequence: 1.4 1.75 2.05 2.5 2.4 Quantization step: 0.2 Predictor: current value = previous quantized value + quantized error. -
Speech Compression
information Review Speech Compression Jerry D. Gibson Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93118, USA; [email protected]; Tel.: +1-805-893-6187 Academic Editor: Khalid Sayood Received: 22 April 2016; Accepted: 30 May 2016; Published: 3 June 2016 Abstract: Speech compression is a key technology underlying digital cellular communications, VoIP, voicemail, and voice response systems. We trace the evolution of speech coding based on the linear prediction model, highlight the key milestones in speech coding, and outline the structures of the most important speech coding standards. Current challenges, future research directions, fundamental limits on performance, and the critical open problem of speech coding for emergency first responders are all discussed. Keywords: speech coding; voice coding; speech coding standards; speech coding performance; linear prediction of speech 1. Introduction Speech coding is a critical technology for digital cellular communications, voice over Internet protocol (VoIP), voice response applications, and videoconferencing systems. In this paper, we present an abridged history of speech compression, a development of the dominant speech compression techniques, and a discussion of selected speech coding standards and their performance. We also discuss the future evolution of speech compression and speech compression research. We specifically develop the connection between rate distortion theory and speech compression, including rate distortion bounds for speech codecs. We use the terms speech compression, speech coding, and voice coding interchangeably in this paper. The voice signal contains not only what is said but also the vocal and aural characteristics of the speaker. As a consequence, it is usually desired to reproduce the voice signal, since we are interested in not only knowing what was said, but also in being able to identify the speaker. -
Entropy Encoding in Wavelet Image Compression
Entropy Encoding in Wavelet Image Compression Myung-Sin Song1 Department of Mathematics and Statistics, Southern Illinois University Edwardsville [email protected] Summary. Entropy encoding which is a way of lossless compression that is done on an image after the quantization stage. It enables to represent an image in a more efficient way with smallest memory for storage or transmission. In this paper we will explore various schemes of entropy encoding and how they work mathematically where it applies. 1 Introduction In the process of wavelet image compression, there are three major steps that makes the compression possible, namely, decomposition, quanti- zation and entropy encoding steps. While quantization may be a lossy step where some quantity of data may be lost and may not be re- covered, entropy encoding enables a lossless compression that further compresses the data. [13], [18], [5] In this paper we discuss various entropy encoding schemes that are used by engineers (in various applications). 1.1 Wavelet Image Compression In wavelet image compression, after the quantization step (see Figure 1) entropy encoding, which is a lossless form of compression is performed on a particular image for more efficient storage. Either 8 bits or 16 bits are required to store a pixel on a digital image. With efficient entropy encoding, we can use a smaller number of bits to represent a pixel in an image; this results in less memory usage to store or even transmit an image. Karhunen-Lo`eve theorem enables us to pick the best basis thus to minimize the entropy and error, to better represent an image for optimal storage or transmission. -
The Pillars of Lossless Compression Algorithms a Road Map and Genealogy Tree
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 6 (2018) pp. 3296-3414 © Research India Publications. http://www.ripublication.com The Pillars of Lossless Compression Algorithms a Road Map and Genealogy Tree Evon Abu-Taieh, PhD Information System Technology Faculty, The University of Jordan, Aqaba, Jordan. Abstract tree is presented in the last section of the paper after presenting the 12 main compression algorithms each with a practical This paper presents the pillars of lossless compression example. algorithms, methods and techniques. The paper counted more than 40 compression algorithms. Although each algorithm is The paper first introduces Shannon–Fano code showing its an independent in its own right, still; these algorithms relation to Shannon (1948), Huffman coding (1952), FANO interrelate genealogically and chronologically. The paper then (1949), Run Length Encoding (1967), Peter's Version (1963), presents the genealogy tree suggested by researcher. The tree Enumerative Coding (1973), LIFO (1976), FiFO Pasco (1976), shows the interrelationships between the 40 algorithms. Also, Stream (1979), P-Based FIFO (1981). Two examples are to be the tree showed the chronological order the algorithms came to presented one for Shannon-Fano Code and the other is for life. The time relation shows the cooperation among the Arithmetic Coding. Next, Huffman code is to be presented scientific society and how the amended each other's work. The with simulation example and algorithm. The third is Lempel- paper presents the 12 pillars researched in this paper, and a Ziv-Welch (LZW) Algorithm which hatched more than 24 comparison table is to be developed. -
The Deep Learning Solutions on Lossless Compression Methods for Alleviating Data Load on Iot Nodes in Smart Cities
sensors Article The Deep Learning Solutions on Lossless Compression Methods for Alleviating Data Load on IoT Nodes in Smart Cities Ammar Nasif *, Zulaiha Ali Othman and Nor Samsiah Sani Center for Artificial Intelligence Technology (CAIT), Faculty of Information Science & Technology, University Kebangsaan Malaysia, Bangi 43600, Malaysia; [email protected] (Z.A.O.); [email protected] (N.S.S.) * Correspondence: [email protected] Abstract: Networking is crucial for smart city projects nowadays, as it offers an environment where people and things are connected. This paper presents a chronology of factors on the development of smart cities, including IoT technologies as network infrastructure. Increasing IoT nodes leads to increasing data flow, which is a potential source of failure for IoT networks. The biggest challenge of IoT networks is that the IoT may have insufficient memory to handle all transaction data within the IoT network. We aim in this paper to propose a potential compression method for reducing IoT network data traffic. Therefore, we investigate various lossless compression algorithms, such as entropy or dictionary-based algorithms, and general compression methods to determine which algorithm or method adheres to the IoT specifications. Furthermore, this study conducts compression experiments using entropy (Huffman, Adaptive Huffman) and Dictionary (LZ77, LZ78) as well as five different types of datasets of the IoT data traffic. Though the above algorithms can alleviate the IoT data traffic, adaptive Huffman gave the best compression algorithm. Therefore, in this paper, Citation: Nasif, A.; Othman, Z.A.; we aim to propose a conceptual compression method for IoT data traffic by improving an adaptive Sani, N.S.