International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 1 (2017) © Research India Publications. http://www.ripublication.com

Performance Assessment of Gaussian Bilateral Filter

Rasool Reddy.K1 Sampurna Lakshmi.P2 Navya Sneha.C1 G.Sukesh1 1 Gudlavalleru Engineering College, Vijayawada, India 2VNRVJIET, Hyderabad, India [email protected] [email protected] [email protected] [email protected]

Abstract. Denoising is one of the important aspects in image processing applications. Denoising is the process of eliminating the from the noisy image. There are numerous denoising approaches are presents and each algorithm has some advantages & disadvantages. After image denoising, quality is one of the main concerns. There are several quality assessments models are present’s to evaluate the quality of an image, in that objective quality assessments is the most prominent models compared to other. This work reviews some of the significant image denoising algorithms such as Gaussian bilateral filter and Gaussian bilateral filtering (GBF) with thresholding approaches in terms quality assessments.

Keywords: Image denoising, Quality Assessments, DWT, Gaussian filter, Bilateral Filter, and Thresholding.

1 Introduction Image processing plays a crucial role in various applications such as radar, satellite, television, medical and industrial applications. While collecting the information from the imagining sensors due to intrinsic (lens arrangement, lens factors) and external parameters (atmosphere, human beings) of the camera device may chance have occurring the noise in the image. Furthermore, noise occurs due to transmission and compression of data. Thus, denoising is a foremost step in any application before analyzes the data. Therefore, it is essential to introduce a well-organized denoising strategy to diminish the noise in data. Denoising is at rest a challenging issue because while removing the noise from data may chance has introduced artifacts and suffers from the blurring. In this work a revision is made on various denoising algorithms and investigates the most prominent approach. In the denoising, information about the type of noise present in the original image plays a major role. Generally, in image processing commonly used are with Gaussian, uniform, or salt & pepper and speckle noise. In this work, mainly focus on the removal of random noise [1] by using different denoising strategies. From early of 20th century, researchers have been focus on denoising and still there is a possibility for enhancement, particularly in image denoising. A simple spatial domain filtering technique (spatial filtering) operated on distorted image, which can be effectively removing the noisy (high frequency) components from distorted image. But, the major problem related to this is, computational complexity. These issues are conquer by transform domain filtering (Low pass filtering) operation. However, due to frequency domain filtering an image to be smoothened overly. To conquer the problems of spatial and frequency domain filtering methodologies authors introduce wavelet based image denoising. are superior to spatial and transform domain strategies because of its multiresolution property [2]. With this popularity in past two decades several wavelet based image denoising methodologies are introduced [3-6]. Later in 1995 the author [7] introduces a wavelet thresholding based denoising approach for removal of random nose. There are two well-known thresholding methods are avail for denoising namely hard-thresholding and soft-thresholding schemes. However, threshold section is major issue in both schemes. Firstly, Donoho provide a universal threshold [7] mechanism based on size of the signal and noise power. Authors [8] were introducing an adaptive thresholding that adapt the image data as well as minimizing the MSE. However, this method performance also depends upon the wavelet coefficients of distorted image. Furthermore, authors [9] provide a Bayesian

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framework using normalized Gaussian distribution. This method provides better Peak Signal to Noise Ratio (PSNR) compared to [7-9]. In 2010, Kother Mohideen et al [10] introduce a new wavelet thresholding method by combing Neighshrink and SureShrink (NeighSureShrink) to reduce the distortion in the image. By overcoming the limitations of VisuShrink and NeighShrink in 2012 Hari Om et al [11] introduce a new wavelet thresholding mechanism based on neighbouring kernel size, which is known as NeighshrinkSure. The rest of the work is presented as: Section II deals with detail description of various existing denoising methods; Section III deals with the detail description of Edge algorithms; Section IV deals with the detail description of results and discussions and Section V deals with the detail description of conclusion.

2 Edge Preserving Filters This section reviews the various edge preserving filtering methodologies such as Gaussian filter and bilateral filter. The main scope of this paper is reducing the noise presents at edges to some large extent.

2.1. Gaussian Filter (GF) Linear filters generates a smoothen image with imperfect noise containment. To conquer these issues introduce a filter based on Gaussian distribution and is called as Gaussian filter. Sometimes GF is also known as non- uniform LPF. The GF is well-known method for removal of noise (Random noise) from images. The GF is attained by simply convolving the Gaussian distribution function with image. The 2D Gaussian distribution is given by 2 2 1 −(x +y ) G (x, y) = e 2σ 2 (1) σ 2πσ2 However, the GF undergo from blurring (Especially at Edges) when the spatial variations are occurs. These issues are eliminated by using bilateral filter [12].

2.2. Bilateral Filter (BF) The BF is a familiar method for image while preserving the edges. It performs filtering operation in both space and range domain. The BF mainly works on the two parameters namely: (1) range and spatial parameters; (2) kernel size. The parameters indicate the contrast and size of the features. These parameters easily to set because of bilateral filter are non-iterative method. In bilateral filter each pixel amplitude restored by average values of neighborhood. Mathematically the bilateral filter at a point „m‟, is defined as 1 퐼 푚 = 퐺 푚 − 푡 퐺 퐼 푚 − 퐼(푡) 퐼(푡) (2) 퐹푖푙푡푒푟푒푑 푤 푡∈푠 휎푠 휎푟 푚 −푡 2 − 2 2휎 푠 Where 퐺휎푠 푚 − 푡 = 푒 represents the geometric closeness 퐼 푚 −퐼(푡) 2 − 2 2휎 푟 퐺휎푟 퐼 푚 − 퐼(푡) = 푒 represents the similarity function W= Normalization Parameters 푚 − 푡 Represents the Euclidian distance between „m‟ and „t‟. and 's‟ is a spatial neighborhood of „t‟.

3 Edge-Preserving Filters and Its Wavelet Thresholding This section describes a system with combination of edge-preserving filters (Gaussian Bilateral) and its wavelet thresholding for denoising of an image. 3.1. Gaussian Bilateral Filter (GBF) and Its Wavelet Thresholding The below figure 1 represents the combination of GBF and wavelet thresholding. From figure, the method noise ‘O’ is obtained by differentiating the source image ‘I’ and filtered image ‘IF’. In general method noise also is a noise. Mathematically, it is given by O = I – IF (3)

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Where ‘I’ represents the source image and ‘IF’ is the filtered version of I. The filtered version of I can achieved by using GBF. The Gaussian Bilateral Filter (GBF) is used to remove the noise as well as detail components by averaging of neighborhood pixel intensities of image, the ‘O’ consists of details, noise as well as edges. Therefore, the method noise ‘O’ is the addition of the (N) and details (D) of image and is given by O = D+N (4)

Figure 1: Framework of GBF and Wavelet Thresholding Now apply DWT on Eq. (7) then we get K = W+ NW (5) Where ‘K’ represents the wavelet coefficients of method noise (O), ‘W’ represents the detail image wavelet coefficients and NW is the independent Gaussian noise. The main aim of wavelet domain is to estimate the true ‘W’ from ‘K’ by using thresholding technique. By selecting the proper threshold we can retain the source image features as well as edges in the denoised image. The estimation of true ‘W’ represents by ‘M’ and its IDWT gives the estimation of image details ‘P’. The addition of ‘M’ and ‘P’ gives the denoised image and is represented by ‘L’. 3.2. Wavelet Thresholding Wavelet thresholding is one of the most prominent techniques for image denoising. There are numerous approaches are avail to estimate the threshold value. In this section we describe few significant thresholding methods. BayesShrink BayesShrink is an adaptive technique and is implemented based on normalized Gaussian distribution. This method provides better performance in terms of PSNR and MSE as compared with SureShrink and VisuShrink. Therefore in this paper BayesShrink is used to find the threshold from noise coefficients. The value of thresholding for minimizing Bayesian risk and is given by 휎2 푇 = (6) 휎푤 2 Where 휎 is the variance of noise component and is estimated from 퐻퐻1 subband by a median estimator is 푀푒푑푖푎푛 퐾 휎 = 푖,푖 , 퐾 ∈ 퐻퐻 (7) 0.6745 푖,푖 1 2 And 휎푤 is the variance of wavelet coefficients and estimated by using following formula 2 2 2 휎 푤 = 푚푎푥 휎 푘 − 휎 , 0 (8) 1 Where 휎 2 = 푀,푁 퐾2 푘 푀푁 푖,푗 =1 푖,푗 Block Shrink Block Shrink [13] is also being a block based thresholding technique. The block shrink is estimate the threshold value and optimal block size for each subband. It is also confines the size of block by using following formula 푁 3/4 1 ≤ 퐿 ≤ [ ] (9) 2푘 Where L gives the size of block; N represents the integer value; K gives the scaling factor. Neigh Shrink Sure

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Authors [14] introduce a new thresholding strategy by conquer the issues of Neigh Shrink [15] and are known as Neigh Shrink SURE. The Neigh Shrink Sure is used to estimate optimal threshold and size of neighboring window for each and every subband by SURE approach. The optimal threshold and subband levels are estimated by using following formula. 푠 푠 휆 ,퐿 = 푎푟푔푚푖푛 푆푈푅퐸 (푤푠, 휆, 퐿) (10) Where λs represents the optimal threshold value for each subband S Ls represent the size of window for each subband S.

4 Quality Metrics In this section we describe various objective image quality metrics to assess the quality of different image denoising strategies. Generally there are three kinds of objective image quality metrics are avail: 1. Full Reference (FR) 2. No Reference (NR) 3. Reduced Reference (RR) In this paper, we consider Full Reference and No Reference quality metrics to assess the quality of an image. The below table 1 represents the list of quality metrics that are used in this work. Table 1. Quality Metrics for Image Denoising S. No Metric Acronym Abbreviation Ref. Description 푀 푁 1 FR NAE Normalized Absolute Error [16] 푖=1 푗 =1 푥푖,푗 − 푦푖,푗 푁퐴퐸 푥, 푦 = 푀 푁 푖=1 푗=1 푥푖,푗 2 FR NK Normalized Cross Correlation [16] 푀 푁 푥 . 푦 푖=1 푗=1 푖,푗 푖,푗 푁퐾 푥, 푦 = 푀 푁 2 푖=1 푗=1 푥푖,푗 3 FR PSNR Peak Signal-to-Noise Ratio [17] 2552 PSNR = 10 log10 MSE M N 1 2 MSE = 푥 − 푦 MN 푖,푗 푖,푗 i=1 j=1 4 FR IQI Image Quality Index [18] See [18] and practical realization in [27] 5 FR MSSSIM Multi Scale Structural Similarity Index Measurement [19] See [19] and practical realization in [27] 6 FR VIF Visual Information Fidelity [20] See [20] and practical realization in [27] 7 FR SR-SIM Spectral Residual – Similarity Index Measurement [21] See [21] and practical realization in [27] 8 FR FSIM Feature Similarity Index Metric [22] See [22] and practical realization in [27] 9 FR RFSIM Riesz-transform Based Feature Similarity Metric [23] See [23] and practical realization in [27] 10 FR MIQM Multicamera image quality measure [24] See [24] and practical realization in [27] 11 FR GMSD Gradient Magnitude Similarity Deviation [25] See [25] and practical realization in [27] 12 NR JQI JPEG Quality Index [26] See [26] and practical realization in [28]

5 Results and Discussions 5.1. Bilateral Filter The below figures [2-13] shows bar plot representation of simulation results of bilateral filter based on different wavelet manager (DWT Managers) in terms of various objective quality parameters. Here, the wavelet packets are used to estimate the noise standard deviation from noisy image. All these simulation results are carried out by using MATLAB R2013a (Ver: 8.1.0.604) software.

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Figure 2: FSIM Figure 3: GMSD

Figure 4: IQI Figure 5: MIQM

Figure 6: MSSSIM Figure 7: NAE

Figure 8: NK Figure 9: PSNR

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Figure 10: RFSIM Figure 11: SR-SIM

Figure 12: VIF Figure 13: JPEG Score As we know as σ increases the error increases and subsequently quality of denoised image is decreases. From the figures [3-13] and table 2 we can say that, bior6.8 wavelet based bilateral filter provide superior performance compared to other wavelet based bilateral filter (Except for GMSD metric) because of Biorthogonal wavelet provides high degree of freedom compared to other orthogonal wavelets like Haar, Daubechies, Colfits and Symlet and this tendency is shown in table 2. The bolded values in the table 2 gives the superior performance compared to all other wavelets. 5.2. Bilateral Filtering and Wavelet Thresholding The below figures [14-25] shows the performance metrics of BF with Block Shrink thresholding based on bior6.8 wavelet package using soft, hard and trimmed thresholding. However, the bior6.8 wavelet provides good performance compared all other wavelet packages such as db8, db16, sym8 and colfit5. From table [3-5] we can say that there is uncertainty occurs while choosing an appropriate method for denoising among bior6.8 based soft, hard and trimmed threshold. Because of by observing the bolded values in the tables, soft thresholding gives good performance in terms of both visuality and structural similarity (PSNR, IQI, VIF, RFSIM and FSIM) at higher values of σ while hard thresholding provide good structural similarity (FSIM, GMSD and SR-SIM) at lower values of σ and whereas trimmed threshold provide good performance in terms of MSSSIM. Therefore, we can say that at lower values of σ bior6.8 soft thresholding where as higher values of σ bior6.8 hard thresholding provide good performance.

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Table 2. Quality Metrics of Bilateral Filter with different standard deviations

Wname σ Parameters NAE NK PSNR IQI MSSSIM VIF FSIM GMSD SR_SIM RFSIM MIQM JPEG

10 0.0472 0.9918 29.2590 0.9855 0.9641 0.4517 0.8761 0.0682 0.9297 0.4175 0.7697 10.2205 20 0.0621 0.9875 26.7770 0.9773 0.9382 0.3448 0.8425 0.0944 0.9093 0.2981 0.7502 10.5042 db8 30 0.0714 0.9860 25.7631 0.9705 0.9151 0.2897 0.8279 0.1114 0.9025 0.2375 0.7500 10.5946 40 0.0801 0.9848 25.0125 0.9628 0.8893 0.2519 0.8165 0.1285 0.8969 0.1941 0.7205 10.5900 50 0.0889 0.9831 24.3175 0.9514 0.8623 0.2226 0.8053 0.1448 0.8892 0.1515 0.6913 10.5457

10 0.0474 0.9917 29.2307 0.9854 0.9639 0.4509 0.8757 0.0685 0.9290 0.4164 0.7704 10.2109 20 0.0621 0.9875 26.7708 0.9773 0.9381 0.3446 0.8423 0.0945 0.9092 0.2979 0.7497 10.5013 db16 30 0.0714 0.9860 25.7559 0.9704 0.9152 0.2896 0.8277 0.1115 0.9023 0.2377 0.7486 10.5856 40 0.0801 0.9848 25.0089 0.9628 0.8896 0.2519 0.8164 0.1285 0.8968 0.1943 0.7195 10.5846 50 0.0889 0.9831 24.3160 0.9542 0.8625 0.2226 0.8052 0.1448 0.8892 0.1520 0.6926 10.5412

10 0.0471 0.9918 29.2861 0.9855 0.9642 0.4524 0.8766 0.0679 0.9295 0.4183 0.7754 10.2324 20 0.0621 0.9875 26.7671 0.9773 0.9381 0.3445 0.8423 0.0945 0.9092 0.2977 0.7464 10.4978 sym8 30 0.0714 0.9860 25.7544 0.9704 0.9152 0.2896 0.8276 0.1115 0.9023 0.2377 0.7489 10.5831 40 0.0801 0.9848 25.0081 0.9628 0.8896 0.2519 0.8163 0.1285 0.8967 0.1944 0.7191 10.5834 50 0.0889 0.9831 24.3140 0.9542 0.8294 0.2226 0.8051 0.1448 0.8891 0.1520 0.6946 10.5371

10 0.0474 0.9917 29.2281 0.9854 0.9639 0.4508 0.8756 0.0685 0.9289 04163 0.7703 10.2093 20 0.0621 0.9875 26.7709 0.9773 0.9381 0.3446 0.8423 0.0945 0.9092 0.2979 0.7497 10.5014 coif5 30 0.0714 0.9860 25.7589 0.9704 0.9151 0.2897 0.8278 0.1115 0.9024 0.2377 0.7507 10.5888 40 0.0801 0.9848 25.0095 0.9628 0.8896 0.2519 0.8164 0.1285 0.8968 0.1944 0.7195 10.5853 50 0.0889 0.9831 24.3153 0.9542 0.8625 0.2226 0.8052 0.1448 0.8892 0.1519 0.6949 10.5418

10 0.0462 0.9922 29.5043 0.9860 0.9656 0.4580 0.8803 0.0658 0.9316 0.4248 0.7809 10.3084 20 0.0614 0.9879 26.9111 0.9778 0.9398 0.3480 0.8458 0.0928 0.9114 0.3011 0.7582 10.5737 bior6.8 30 0.0711 0.9862 25.8284 0.9707 0.9159 0.2910 0.8300 0.1108 0.9040 0.2387 0.7517 10.6670 40 0.0800 0.9850 25.0446 0.9627 0.8913 0.2522 0.8179 0.1282 0.8978 0.1933 0.7295 10.6346 50 0.0890 0.9833 24.3300 0.9538 0.8617 0.2225 0.8061 0.1449 0.8899 0.1509 0.6907 10.5893

Figure 14: PSNR Figure 15: IQI

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Figure 16: NAE Figure 17: NK

Figure 18: VIF Figure 19: FSIM

Figure 20: GMSD Figure 21: SR-SIM

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Figure 22: RFSIM Figure 23: MSSSIM

Figure 24: MIQM Figure 25: JPEG Score

Table 3. Quality Metrics of BF with BlockShrink based on bior6.8 soft thresholding Parameters σ 10 20 30 40 50 PSNR 32.849 28.9489 26.9252 25.4907 24.4584 IQI 0.9871 0.9787 0.9706 0.9595 0.9501 NAE 0.0406 0.0568 0.067 0.0785 0.089 NK 0.995 0.9923 0.9918 0.99 0.9873 JPEG Score 9.9887 10.3593 10.3591 10.3391 10.2416 VIF 0.8278 0.6916 0.5899 0.5034 0.4416 FSIM 0.9098 0.8696 0.8566 0.8346 0.8167 GMSD 0.0532 0.0877 0.1158 0.1398 0.1544 SR-SIM 0.9519 0.9284 0.9228 0.9136 0.9028 RFSIM 0.4467 0.3081 0.2388 0.1751 0.1274 MSSSIM 0.9793 0.9476 0.9149 0.8813 0.8481 MIQM 0.9642 0.9123 0.8432 0.8123 0.7952

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Table 4. Quality Metrics of BF with BlockShrink based on bior6.8 hard thresholding Parameters σ 10 20 30 40 50 PSNR 30.9127 28.1744 26.2571 24.6641 23.2285 IQI 0.9863 0.9784 0.9638 0.9478 0.9336 NAE 0.0414 0.0564 0.0728 0.0882 0.1056 NK 0.9963 0.9947 0.9947 0.9924 0.9901 JPEG Score 9.8508 9.9966 9.7921 9.8206 9.571 VIF 0.8386 0.6946 0.58 0.4894 0.4208 FSIM 0.9197 0.8815 0.8518 0.818 0.7805 GMSD 0.0543 0.095 0.1383 0.1656 0.1875 SR-SIM 0.9586 0.9377 0.9237 0.9044 0.8804 RFSIM 0.4343 0.3072 0.2034 0.1386 0.0834 MSSSIM 0.9755 0.9502 0.9142 0.8747 0.8298 MIQM 0.9209 0.8567 0.8114 0.766 0.7219

Table 5. Quality Metrics of BF with BlockShrink based on bior6.8 trimmed thresholding Parameters σ 10 20 30 40 50 PSNR 30.9631 28.0701 26.7742 25.4114 24.3332 IQI 0.9869 0.9787 0.9693 0.9571 0.9463 NAE 0.0404 0.0562 0.0675 0.08 0.0917 NK 0.9957 0.9932 0.9929 0.991 0.9883 JPEG Score 9.9077 10.255 10.2015 10.1904 10.0569 VIF 0.8362 0.6951 0.5883 0.5004 0.4395 FSIM 0.9152 0.8749 0.8595 0.834 0.8127 GMSD 0.0525 0.0897 0.1227 0.1467 0.1605 SR-SIM 0.9553 0.9324 0.9255 0.9143 0.9009 RFSIM 0.444 0.3116 0.235 0.1699 0.1166 MSSSIM 0.9766 0.9504 0.9231 0.8892 0.8569 MIQM 0.8724 0.8339 0.8057 0.7601 0.6943

5.3. Bilateral Filter with NeighShrinkSURE Thresholding From the result of table [6-10] we can say that, sym8 based bilateral filter with NeighShrinkSURE gives superior performance than other wavelet package in terms of visual information(VIF) and structural similarity (MSSSIM, FSIM,RFSIM and SR-SIM).

Table 6. Quality Metrics of BF with NeighShrinkSURE based on db8 Parameters σ 10 20 30 40 50 PSNR 32.8819 28.8747 26.686 25.1505 23.9885 IQI 0.9921 0.9805 0.9688 0.9571 0.9451 NAE 0.0339 0.0536 0.069 0.0828 0.0955 NK 0.9974 0.9945 0.9919 0.9894 0.9865 JPEG Score 10.5709 10.9892 11.0369 11.0147 10.8807 VIF 0.8634 0.7008 0.5862 0.5031 0.4418 FSIM 0.9478 0.8986 0.8627 0.834 0.8102 GMSD 0.036 0.0783 0.1085 0.1315 0.1509 SR-SIM 0.9738 0.9474 0.9278 0.9112 0.896 RFSIM 0.5105 0.3232 0.2252 0.1621 0.1157 MSSSIM 0.9742 0.946 0.9128 0.8846 0.8459 MIQM 0.9293 0.8691 0.8239 0.7432 0.7037

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Table 7. Quality Metrics of BF with NeighShrinkSURE based on db16 Parameters σ 10 20 30 40 50 PSNR 32.9131 28.8612 26.5954 25.1231 23.9738 IQI 0.9925 0.9806 0.9683 0.956 0.9448 NAE 0.0339 0.0538 0.0698 0.0832 0.0957 NK 0.9975 0.9945 0.9918 0.9894 0.9865 JPEG Score 10.4679 10.7736 10.8878 10.859 10.776 VIF 0.8623 0.6935 0.58 0.4971 0.4366 FSIM 0.9482 0.8989 0.8605 0.8337 0.81 GMSD 0.0367 0.0787 0.11 0.1329 0.1507 SR-SIM 0.9751 0.9486 0.9264 0.9098 0.8938 RFSIM 0.5094 0.319 0.219 0.158 0.112 MSSSIM 0.9739 0.941 0.9058 0.8831 0.8411 MIQM 0.9197 0.8758 0.8165 0.7597 0.7059

Table 8. Quality Metrics of BF with NeighShrinkSURE based on sym8 Parameters σ 10 20 30 40 50 PSNR 32.9745 28.987 26.7357 25.1992 24.032 IQI 0.9924 0.981 0.9688 0.9563 0.9447 NAE 0.0334 0.0528 0.0684 0.0824 0.0952 NK 0.9975 0.9946 0.9919 0.9895 0.9866 JPEG Score 10.5166 10.8606 10.9632 10.9579 10.7824 VIF 0.8671 0.7047 0.5892 0.5037 0.4416 FSIM 0.9489 0.901 0.8648 0.8368 0.8137 GMSD 0.036 0.0767 0.1065 0.1306 0.1507 SR-SIM 0.9752 0.9491 0.9288 0.9124 0.8966 RFSIM 0.5157 0.3253 0.2258 0.1592 0.1122 MSSSIM 0.985 0.959 0.9294 0.8976 0.8569 MIQM 0.9254 0.8706 0.8327 0.7701 0.6962

Table 9. Quality Metrics of BF with NeighShrinkSURE based on coif5 Parameters σ 10 20 30 40 50 PSNR 32.9456 28.9568 26.7202 25.172 23.9967 IQI 0.9924 0.9815 0.9686 0.9557 0.9446 NAE 0.0336 0.0531 0.0687 0.0827 0.0955 NK 0.9975 0.9946 0.9921 0.9895 0.9866 JPEG Score 10.2589 10.5693 10.6696 10.6396 10.5645 VIF 0.8632 0.6997 0.5869 0.5006 0.4368 FSIM 0.9485 0.9012 0.8643 0.835 0.8118 GMSD 0.0359 0.0758 0.1059 0.1304 0.15 SR-SIM 0.9749 0.9506 0.9285 0.9085 0.8939 RFSIM 0.5118 0.3215 0.2215 0.1561 0.1081 MSSSIM 0.9847 0.9579 0.9284 0.8958 0.8635 MIQM 0.9233 0.8782 0.829 0.7706 0.6915

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Table 10. Quality Metrics of BF with NeighShrinkSURE based on bior6.8 Parameters σ 10 20 30 40 50 PSNR 32.8039 28.74 26.5172 24.9903 23.8176 IQI 0.9923 0.98 0.9665 0.9535 0.9412 NAE 0.0342 0.0546 0.071 0.0854 0.0984 NK 0.9975 0.9947 0.9923 0.9899 0.9869 JPEG Score 10.3766 10.6678 10.6394 10.594 10.4777 VIF 0.8645 0.7017 0.5866 0.5043 0.4409 FSIM 0.9472 0.8966 0.859 0.8297 0.8059 GMSD 0.0362 0.0777 0.1084 0.1325 0.1522 SR-SIM 0.9746 0.947 0.9273 0.9107 0.8962 RFSIM 0.5032 0.3103 0.2125 0.1469 0.102 MSSSIM 0.9841 0.9559 0.9256 0.8933 0.8607 MIQM 0.9234 0.8767 0.8244 0.7452 0.6971

5.4. GBF With BayesShrink Threshold The tables [11-13] represent the performance of GBF with BayesShrink using wavelet package based on soft/hard/trimmed thresholding in terms of image quality metrics/attributes. From tables [11-13] we can say that the GBF with BayesShrink Based on soft thresholding. From table 11 we can say that, the coif5 provide superior performance in terms of PSNR, IQI and SSIM, where as bior6.8 provided superior information in terms of FSIM, SR- SIM and MIQM compared to others. The IQI and SSIM are not adapting the HVS to estimate the structural information in the images while in FSIM and SR-SIM adapts the HVS to estimate the information in image data. Therefore, bior6.8 based soft thresholding is superior information compared to all other wavelet strategies. The below figure 26 shows the source image for image denoising with 256×256 resolution.

Figure 26: Source Image

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Table 11. Performance metrics of GBF using BayesShrink based on soft thresholding

Wname σ Parameters NAE NK PSNR IQI MSSSIM VIF FSIM GMSD SR_SIM RFSIM MIQM JPEG

10 0.0357 0.9977 32.5605 0.9907 0.9832 0.5240 0.9431 0.0379 0.9724 0.4965 0.9069 10.5614 20 0.0540 0.9943 28.7492 0.9799 0.9553 0.3802 0.8935 0.0788 0.9432 0.3215 0.8563 10.6966 db8 30 0.0683 0.9905 26.5738 0.9701 0.9219 0.2971 0.8538 0.1104 0.9230 0.2303 0.7948 10.8292 40 0.0788 0.9881 25.3505 0.9611 0.8928 0.2526 0.8274 0.1321 0.9071 0.1785 0.7260 10.6683 50 0.0887 0.9955 24.4189 0.9518 0.8631 0.2205 0.8089 0.1504 0.8923 0.1360 0.6830 10.5649

10 0.0359 0.9976 32.5362 0.9908 0.9827 0.5237 0.9425 0.0390 0.9725 0.4925 0.9102 10.2992 20 0.0544 0.9941 28.6914 0.9795 0.9538 0.3777 0.8920 0.0826 0.9454 0.3191 0.8549 10.2528 db16 30 0.0688 0.9904 26.5287 0.9697 0.9211 0.2941 0.8531 0.1118 0.9224 0.2267 0.8002 10.2641 40 0.0794 0.9881 25.2974 0.9606 0.8907 0.2492 0.8268 0.1336 0.9059 0.1742 0.7393 10.2754 50 0.0891 0.9856 24.3958 0.9516 0.8617 0.2183 0.8085 0.1509 0.8930 0.1342 0.6689 10.2969

10 0.0355 0.9977 29.2622 0.9907 0.9835 0.8719 0.9440 0.0373 0.9724 0.5079 0.9132 10.3306 20 0.0533 0.9943 28.8231 0.9799 0.9562 0.7039 0.8950 0.0778 0.9444 0.3292 0.8574 10.3816 sym8 30 0.0679 0.9906 26.6072 0.9703 0.9239 0.5665 0.8549 0.1103 0.9216 0.2312 0.7983 10.4501 40 0.0785 0.9881 25.3665 0.9613 0.8942 0.4908 0.8284 0.1326 0.9064 0.1777 0.7380 10.5520 50 0.0885 0.9855 24.4341 0.9521 0.8640 0.4355 0.8094 0.1501 0.8955 0.1350 0.6796 10.5464

10 0.0352 0.9977 32.6592 0.9913 0.9835 0.5279 0.9438 0.0369 0.9724 0.5002 0.9092 9.8565 20 0.0530 0.9944 28.8671 0.9802 0.9564 0.3840 0.8952 0.0784 0.9464 0.3287 0.8635 9.8004 coif5 30 0.0677 0.9907 26.6488 0.9708 0.9240 0.2984 0.8544 0.1104 0.9214 0.2327 0.8118 9.9644 40 0.0785 0.9883 25.3881 0.9618 0.8940 0.2526 0.8290 0.1324 0.9076 0.1787 0.7591 10.1296 50 0.0886 0.9857 24.4323 0.9523 0.8629 0.2199 0.8096 0.1570 0.8953 0.1341 0.6837 10.2200

10 0.0365 0.9981 32.4491 0.9905 0.9826 0.5209 0.9422 0.0388 0.9730 0.4888 0.9100 9.9694 20 0.0553 0.9955 28.7365 0.9785 0.9531 0.3794 0.8924 0.0832 0.9471 0.3167 0.8661 9.8126 bior6.8 30 0.0696 0.9928 26.6864 0.9672 0.9213 0.2992 0.8566 0.1145 0.9266 0.2207 0.8061 9.8026 40 0.0825 0.9897 25.2050 0.9563 0.8880 0.2453 0.8276 0.1379 0.9091 0.1610 0.7188 9.8629 50 0.0935 0.9871 24.1765 0.9454 0.8568 0.2124 0.8071 0.1565 0.8959 0.1162 0.6833 9.8674

Figure 27: GBF with BayesShrink using Trimmed threshold

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Table 12. Performance metrics of GBF using BayesShrink based on hard thresholding Wname σ Parameters NAE NK PSNR IQI MSSSIM VIF FSIM GMSD SR_SIM RFSIM MIQM JPEG

10 0.0474 0.9993 30.3604 0.9836 0.9779 0.4724 0.9207 0.0489 0.9644 0.3939 0.8595 10.1964 20 0.0687 0.9975 26.9869 0.9677 0.9430 0.3429 0.8585 0.1024 0.9314 0.2371 0.7924 10.3763 db8 30 0.0811 0.9936 25.4329 0.9565 0.9097 0.2671 0.8267 0.1306 0.9049 0.1676 0.7284 10.8282 40 0.0877 0.9899 24.6234 0.9513 0.8827 0.2302 0.8118 0.1439 0.9004 0.1396 0.6983 10.7325 50 0.0907 0.9864 24.2667 0.9490 0.8611 0.2152 0.8065 0.1535 0.8943 0.1273 0.6850 10.5962

10 0.0471 0.9993 30.4359 0.9837 0.9771 0.4742 0.9212 0.0495 0.9643 0.3934 0.8669 10.0216 20 0.0678 0.9973 27.1609 0.9683 0.9403 0.3462 0.8581 0.1072 0.9319 0.2397 0.7965 9.9633 db16 30 0.0809 0.9933 25.5313 0.9568 0.9037 0.2660 0.8218 0.1351 0.9102 0.1679 0.7235 10.0321 40 0.0881 0.9899 24.6624 0.9512 0.8783 0.2289 0.8108 0.1506 0.8984 0.1371 0.7072 10.0504 50 0.0930 0.9865 24.1450 0.9465 0.8549 0.2099 0.8019 0.1575 0.8894 0.1190 0.6960 10.1684

10 0.0472 0.9994 30.3323 0.9835 0.9769 0.8734 0.9210 0.0487 0.9644 0.3955 0.8720 9.9694 20 0.0666 0.9975 27.1732 0.9685 0.9418 0.7047 0.8630 0.1008 0.9317 0.2490 0.8025 9.9558 sym8 30 0.0800 0.9934 25.4950 0.9584 0.9065 0.5651 0.8298 0.1309 0.9105 0.1800 0.7482 10.1660 40 0.0859 0.9898 24.6989 0.9534 0.8826 0.4877 0.8162 0.1454 0.9012 0.1489 0.7140 10.4145 50 0.0900 0.9864 24.2842 0.9499 0.8628 0.4351 0.8089 0.1536 0.8938 0.1269 0.6748 10.4903

10 0.0463 0.9993 30.4920 0.9836 0.9765 0.4762 0.9218 0.0491 0.9648 0.4030 0.8612 9.6188 20 0.0659 0.9975 27.2794 0.9701 0.9390 0.3507 0.8628 0.1041 0.9341 0.2500 0.8104 9.2810 coif5 30 0.0785 0.9937 25.6881 0.9601 0.9050 0.2707 0.8297 0.1329 0.9117 0.1799 0.7444 9.3387 40 0.0854 0.9901 24.7851 0.9531 0.8837 0.2333 0.8187 0.1441 0.9017 0.1475 0.7224 9.7338 50 0.0906 0.9868 24.2690 0.9498 0.8605 0.2147 0.8084 0.1553 0.8946 0.1264 0.6776 10.0239

10 0.0493 0.9995 29.9906 0.9819 0.9751 0.4653 0.9516 0.0504 0.9621 0.3814 0.8542 9.6914 20 0.0795 0.9984 25.6546 0.9589 0.9296 0.3230 0.8365 0.1144 0.9206 0.1953 0.7469 9.0728 bior6.8 30 0.1024 0.9968 23.3558 0.9394 0.8821 0.2476 0.7820 0.1550 0.8889 0.1135 0.6493 8.7182 40 0.1215 0.9929 21.7717 0.9229 0.8377 0.1922 0.7414 0.1778 0.8377 0.0727 0.5717 8.5106 50 0.1424 0.9898 20.3449 0.9060 0.7947 0.1583 0.7092 0.1995 0.7947 0.0433 0.5164 8.3269

Figure 28: GBF with BayesShrink using Soft threshold Figure 29: GBF with BayesShrink using hard threshold

The figures [27-29] can be achieved by setting following parameters. 1. σs =1.8 2. σr =5σn 3. kernel size=11 × 11 and 4. Wavelet Type = db16

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Table 13. Performance metrics of GBF using BayesShrink based on trimmed thresholding Wname σ Parameters NAE NK PSNR IQI MSSSIM VIF FSIM GMSD SR_SIM RFSIM MIQM JPEG

10 0.0386 0.9986 32.0370 0.9890 0.9820 0.5110 0.9378 0.0421 0.9713 0.4675 0.9033 10.4799 20 0.0568 0.9985 28.4900 0.9768 0.9533 0.3723 0.8876 0.0847 0.9425 0.3010 0.8569 10.6610 db8 30 0.0703 0.9915 26.4612 0.9675 0.9220 0.2301 0.8524 0.1135 0.9230 0.2160 0.7974 10.8620 40 0.0796 0.9887 25.3310 0.9601 0.8921 0.2500 0.8277 0.1333 0.9084 0.1737 0.7863 10.7090 50 0.0888 0.9857 24.4296 0.9515 0.8633 0.2203 0.8097 0.1503 0.8934 0.1352 0.6951 10.5572

10 0.0387 0.9986 32.0477 0.9890 0.9811 0.5112 0.9371 0.0434 0.9708 0.4650 0.8967 10.2160 20 0.0572 0.9956 28.4669 0.9766 0.9507 0.3711 0.8855 0.0898 0.9436 0.2988 0.8508 10.1674 db16 30 0.0708 0.9914 26.4315 0.9668 0.9181 0.2877 0.8505 0.1164 0.9225 0.2131 0.7951 10.1886 40 0.0803 0.9886 25.2771 0.9592 0.8903 0.2466 0.8271 0.1359 0.9064 0.1679 0.7358 10.2273 50 0.0892 0.9858 24.4067 0.9509 0.8613 0.2178 0.8088 0.1513 0.1679 0.1338 0.6739 10.2735

10 0.0384 0.9987 32.0527 0.9888 0.9814 0.8747 0.9386 0.0416 0.9713 0.4745 0.8925 10.2102 20 0.0560 0.9959 28.5762 0.9772 0.9534 0.7170 0.8901 0.0835 0.9433 0.3116 0.8446 10.2806 sym8 30 0.0697 0.9916 26.4953 0.9680 0.9219 0.5687 0.8542 0.1135 0.9226 0.2203 0.7844 10.3612 40 0.0790 0.9886 25.3508 0.9607 0.0930 0.4911 0.8297 0.1339 0.9073 0.1728 0.7314 10.5228 50 0.0884 0.9857 24.3508 0.9514 0.8648 0.4358 0.8108 0.1501 0.8959 0.1347 0.6818 10.5417

10 0.0379 0.9987 32.1443 0.9896 0.9812 0.5152 0.9387 0.0418 0.9716 0.4812 0.8906 9.7378 20 0.0556 0.9960 28.6430 0.9779 0.9516 0.3775 0.8906 0.0853 0.9456 0.3516 0.8430 9.5959 coif5 30 0.0692 0.9917 26.5722 0.9690 0.9217 0.2927 0.8540 0.1142 0.9212 0.2217 0.8087 9.7822 40 0.0789 0.9889 25.3879 0.9609 0.8937 0.2508 0.8307 0.1332 0.9085 0.1937 0.7627 10.0309 50 0.0884 0.9859 24.4701 0.9522 0.8635 0.2203 0.8190 0.1511 0.8963 0.0635 0.6853 10.1836

10 0.0404 0.9989 31.6449 0.9879 0.9796 0.5029 0.9337 0.0443 0.9701 0.4529 0.8912 9.8125 20 0.0612 0.9970 27.9646 0.9739 0.9457 0.3644 0.8775 0.0949 0.9412 0.2793 0.8234 9.5384 bior6.8 30 0.0765 0.9945 25.9617 0.9609 0.9117 0.2854 0.8401 0.1263 0.9197 0.1896 0.7568 9.4419 40 0.0897 0.9908 24.5294 0.9493 0.8769 0.2307 0.8110 0.1484 0.8996 0.1350 0.6894 9.4633 50 0.1014 0.9879 24.3300 0.9373 0.8411 0.1987 0.7896 0.1661 0.8852 0.0963 0.6750 9.4360

6. Conclusion In this work, a GBF with wavelet thresholding has been proposed. From simulation results of GBF with NeighShrinkSure is provide good performance compared to other wavelet thresholding. The GBF with Neighshrink sure using bior6.8 wavelet transform provides good performance compared to all other strategies in terms of PSNR. SSIM, FSIM, IQI and MIQM. The performance of GBF with Neighshrink sure using bior6.8 can be improved strategy by estimating optimal threshold and size of neighboring window for each and every subband by SURE approach using NeighShrinkSure. In future this concept is extended for Non-local means filtering approaches and real time images.

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