HD Photo反馈式编码及图像后处理技术研究
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摘要
HD Photo是由微软公司开发的一种新的静止图像压缩算法和文件格式,目前已经通过JPEG组织提案,有望成为第三代国际图像压缩标准。HD Photo能在同一系统中实现无损压缩和有损压缩,并且在保持较高的压缩质量的前提下,降低计算复杂度和内存消耗。HD Photo支持对感兴趣区域的编解码,支持缩略图的提取,其压缩质量优于JPEG,压缩性能堪比JPEG2000。本文在HD Photo压缩标准的基础上,从以下几个方面做了深入的研究:
首先,对HD Photo中的PCT和POT变换做了深入的研究,对两点的旋转变换,一维四点的旋转变换,二维四点的旋转变换和一维四点的滤波操作进行了提升实现和数学推导,给出了变换的效果图。
其次,在HD Photo压缩标准的基础上,提出了基于多尺度结构相似度准则的HD Photo反馈式编码方法。将解码图像与原图像的结构相似度差值反馈于编码时采用的量化系数,实现量化系数的自适应调整。实验结果表明,较之量化系数固定的HD Photo压缩算法,该方法能够提高解码图像的主观视觉质量。
最后,针对目前HD Photo压缩算法中没有加入图像后处理技术,对于高压缩比情况下HD Photo解码图像块效应问题,提出了两种去除块效应的方法。第一种是基于2D双树复数小波硬阈值的块效应去除算法,第二种是基于块匹配和三维滤波的块效应去除算法。实验结果表明,两种算法都能够很好的减弱图像的块效应,并且保留了较多的细节信息,提高图像的主观视觉质量。
HD Photo is a new still-image compression algorithm and file format, developed and patented by Microsoft, and now is under consideration in JPEG committee as the third generation international image compression standard. HD Photo can realize both lossless and lossy compression in the same system, it merits in terms of compression ratio and coding quality with occupying much less memory space. HD Photo supports coding of the region of interest, thumbnail extraction. HD Photo is better than JPEG in compression quality while its compression efficiency is the same as JPEG. Based on the HD Photo compression standard, this paper is composed of the following content:
First of all, this paper does some further research on PCT and POT transform included in HD Photo, makes implementation of the two points rotation, one-dimensional four points rotation, two-dimensional rotation and one-dimensional four points overlap operation based on lifting, and derivates the formula particularly. Finally, the effect figures are given.
Secondly, based on HD Photo compression standard, a method on feedback coding based on Multi-Scale Structural Similarity criterion is proposed. The algorithm calculates the error of reconstruct image and the original image, then uses it to adjust the quant scale used in coding, realizing the adaptive quantization. The experiment results show, compared to the HD Photo’s compression algorithm, the proposed scheme improves subjective visual quality of the coded image.
At last, HD Photo compression standard has no image post-processing technology; the decoded image will generate block effect in high compression ratio. In order to solve the problem, two algorithms are proposed to eliminate image block effect. One method is based on 2D dual-tree complex wavelet and hard threshold, another method is based on block matching and 3D filtering. The experiment results show that both of the two algorithms can eliminate block effect while maintaining some image details, and can improve the subjective visual quality of the image.
首先,对HD Photo中的PCT和POT变换做了深入的研究,对两点的旋转变换,一维四点的旋转变换,二维四点的旋转变换和一维四点的滤波操作进行了提升实现和数学推导,给出了变换的效果图。
其次,在HD Photo压缩标准的基础上,提出了基于多尺度结构相似度准则的HD Photo反馈式编码方法。将解码图像与原图像的结构相似度差值反馈于编码时采用的量化系数,实现量化系数的自适应调整。实验结果表明,较之量化系数固定的HD Photo压缩算法,该方法能够提高解码图像的主观视觉质量。
最后,针对目前HD Photo压缩算法中没有加入图像后处理技术,对于高压缩比情况下HD Photo解码图像块效应问题,提出了两种去除块效应的方法。第一种是基于2D双树复数小波硬阈值的块效应去除算法,第二种是基于块匹配和三维滤波的块效应去除算法。实验结果表明,两种算法都能够很好的减弱图像的块效应,并且保留了较多的细节信息,提高图像的主观视觉质量。
HD Photo is a new still-image compression algorithm and file format, developed and patented by Microsoft, and now is under consideration in JPEG committee as the third generation international image compression standard. HD Photo can realize both lossless and lossy compression in the same system, it merits in terms of compression ratio and coding quality with occupying much less memory space. HD Photo supports coding of the region of interest, thumbnail extraction. HD Photo is better than JPEG in compression quality while its compression efficiency is the same as JPEG. Based on the HD Photo compression standard, this paper is composed of the following content:
First of all, this paper does some further research on PCT and POT transform included in HD Photo, makes implementation of the two points rotation, one-dimensional four points rotation, two-dimensional rotation and one-dimensional four points overlap operation based on lifting, and derivates the formula particularly. Finally, the effect figures are given.
Secondly, based on HD Photo compression standard, a method on feedback coding based on Multi-Scale Structural Similarity criterion is proposed. The algorithm calculates the error of reconstruct image and the original image, then uses it to adjust the quant scale used in coding, realizing the adaptive quantization. The experiment results show, compared to the HD Photo’s compression algorithm, the proposed scheme improves subjective visual quality of the coded image.
At last, HD Photo compression standard has no image post-processing technology; the decoded image will generate block effect in high compression ratio. In order to solve the problem, two algorithms are proposed to eliminate image block effect. One method is based on 2D dual-tree complex wavelet and hard threshold, another method is based on block matching and 3D filtering. The experiment results show that both of the two algorithms can eliminate block effect while maintaining some image details, and can improve the subjective visual quality of the image.
引文
1胡栋.静止图像编码的基本方法与国际标准.北京:北京邮电大学出版社,2003:121-165
2 L. Zhang, W. Gao, Q.Wang, et al. Macroblock-Level Adaptive Scan Scheme for Discrete Cosine Transform Coefficients. Proc. IEEE Int. on Symp. Circuits and Systems, 2007:537-540
3 R. C. Gonzalez, R. E. Woods, S. L. Eddins.数字图像处理.阮秋琦.北京.电子工业出版社,2005:245-251
4张贤达.现代信号处理.第二版.北京:清华大学出版社,2002:378-390
5 D. F. Mix, K. J. Olejniczak.小波基础及应用教程.杨志华,杨力华.北京:机械工业出版, 2006:113-126
6 D. Taubman. High performance scalable image compression with EBCOT. IEEE Tram. on Image Processing, 2000, 9171: 1158-1170
7 C. J. Lian, K. F. Chen. H. H. Chela. Analysis and architecture design of block-coding engine for EBCOT in JPEG2000. IEEE Trans. On Circuits and Systems for Video Tchnology. 2003,13(3): 219-230
8 S. Srinivasan, C. Tu, S. L. Regunathan, et al. HD Photo: A new image coding technology for digital photography. Proc. SPIE Appl. of Digital Image Processing, 2007,6696:1-7
9 ITU-T SG16 Q.6 and ISO/IEC JTC 1/SC 29 WG1. Study Text for JPEG XR FCD (ISO/IEC 29199-2), Document N4659,2008:1-75
10 F. Dufaux, G. J. Sullivan, T. Ebrahimi. The JPEG XR Image Coding Standard. IEEE Signal Processing Magzine,2009,26(6):195-204 204-204
11 Zhang Li-bao, Wang Ke. Embedded multiple subbands scaling image coding using reversible integer wavelet transforms. Proceedings of 2004 International Symposium on Intelligent Multimedia, Video and Speech Processing, 2001,(1):201-204
12 A. R. Calderbank, I. Daubechies, W. Sweldens, et al. Lossless image compression using integer to integer wavelet transforms, Proc.IEEE ICIP, 1997,10:596-599
13 Hao Xu, Jizheng Xu, Feng Wu. Lifting-Based Directional DCT-Like Transform for Image Coding. IEEE Transactions on Circuits and Systems for Video Technology, 2001,17(10):1325-1335
14 Lei Wang, Jiaji Wu, Licheng Jiao, et al. Lossy to lossless image compression based on reversible integer DCT. 15th IEEE International Conference on Image Processing, 2008:1037-1040
15 A. Maalouf, M. C. Larabi. Low-complexity enhanced lapped transform for image coding in JPEG XR/HD Photo.16th IEEE International Conference on Image Processing (ICIP), 2009:5-8
16 H. S. Malvar. Efficient signal coding with hierarchical lapped transforms. International Conference on Acoustics, Speech, and Signal Processing, 1990,3: 1519-1522
17 Jizheng Xu, Feng Wu, Jie Liang, et al. Directional Lapped Transforms for Image Coding. Proc. IEEE Transactions on Image Processing, 2010,19:85-97
18 A. A. Skodras, A. N. Skodras. Compression of confocal microscopy images: a comparative study. Proc. of SPIE, 2008, 7008I:1-8
19 F. D. Simone, M. Ouaret, F. Dufaux, A. G. Tescher. A comparative study of JPEG2000, AVC/H.264, and HD photo. Proc. SPIE, 2007, 669602:1-11
20 Microsoft Corp.. HD Photo Specification and HD Photo Device Porting Kit 1.0, http://www.microsoft.com/windows/windowsmedia/forpros/wmphoto/, 2006
21 H. C. Reeve, J. S. Lim. Reduction of blocking effect in image coding. Proc.ICASSP Boston, 1983:1212-1215
22 T. D. Tran, Jie Liang, Chengjie Tu. Lapped Transform via Time-Domain Pre- and Post-Filtering. IEEE transaction on signal processing, 2003,51(6):1557-1571
23 H. S. Malvar, D. H. Staelin. The LOT: transform coding without blocking effects. IEEE Trans. on Acoustics Speech, and Signal Processing, 1989,37:553-559
24 H. S. Malvar. Biorthogonal and nonuniform lapped transforms for transform codingwith reduced blocking and ringing artifacts. IEEE Transaction Signal Processing, 1998:1043-1053
25 Bill Crow’s HD Photo Blog: http://blogs.msdn.com/billcrow/default.aspx,2007
26 S. H. Groder, K. W. Hsu. Design methodolgy for HD Photo compression algorithm targeting a FPGA. 2008 IEEE International SOC Conference, 2008:105-108
27 C. C. Juan, J. B. Michael, C.S. Eagle. Vulnerability Analysis of HD Photo Image Viewer Applications. Second International Conference on Secure System Integration and Reliability Improvement, 2008:1-7 14-17
28 H. S. Malvar, G. J. Sullivan, S. Srinivasan. Lifting-based reversible color transforma- tions for image compression. Proc. SPIE, 2008, 707307:1-10
29 C. J. Tu, S. Srinivasan, G. J. Sullivan. Low-complexity hierarchical lapped transform for lossy-to-lossless image coding in JPEG XR/HD Photo. Proc. of SPIE. 2008, 70730C:1-12
30 S. Srinivasan, Z. Zhou, G. J. Sullivan, et al. Coding of High Dynamic Range Images in JPEG XR/HD Photo. Proc. of SPIE, 2008, 707315:1-9
31 D. Schonberg, S .J. Sun, G. J. Sullivan. Techniques for enhancing JPEG XR/HD Photo rate-distortion performance for particular fidelity metrics. Proc. of SPIE, 2008, 707314:1-10
32 H. Koichi, T. Hiroshi, O. Hiroyuki, et al. Architecture of photo core transform in HD photo coding system for embedded systems of various bandwidths. Proc. IEEE Asia Pacific Conf. on Circuits and Systems, 2008:1592-1595
33 T. Suzuki, M. ikehara. Realization of lossless-to-lossy image coding compatible with JPEG standard by direct-lifting of DCT-IDCT. Processing of 2010 IEEE 17th international conference on image processing, Hong Kong ,2010:26-29 389-392
34许君一,孙伟,齐旭东.矩阵Kronecker乘积及其应用.计算机辅助设计与图形学学报,2003,4(15):378-388
35 M. P. Eckert, A. P. Bradley. Perceptual quality metrics applied to still image Compression. Signal Processing Volume, 1998,3(30):177-200
36 J. L. Mannos, D. J. Sakrison. The effects of a visual fidelity criterion on the encodingof Images. IEEE Trans. Inform. Theory, 1974,IT-4:525-536
37 Watson, L. Kreslake. Measurement of visual impairment scales for digital video. Proc. SPIE-Human Vision, Visual Processing, and Digital Display,2001,4299:1-7
38 G. Ramos, S. S. Hemami. Suprathreshold wavelet coefficient quantization in complex stimuli, psychophysical evaluation and analysis, 2001,18:2385-2397
39 D. M. Chandler, S. S. Hemami. Additivity models for suprathreshold distortion in quantized wavelet-coded images. SPIE-Human Vision and Electronic Imaging VII, 2002,4662:1-11
40 A. B. Watson.Visual detection of spatial contrast patterns: evaluation of five simple models. 2000,6:12-33
41 E. P. Simoncelli. Statistical models for images: compression, restoration and synthesis. Proc. 31st Asilomar Conf. Signals, Systems and Computers, Pacific Grove, CA, 1997, 11: 673-678
42 Z. Wang, A. C. Bovik. Embedded foveation image coding. IEEE Trans. Image Processing, 2001,10:1397-1410
43 Z. Wang, A. C. Bovik. A universal image quality index. IEEE Signal Processing Letters, 2002,9:81-84
44 Z. Wang, A. C. Bovik, H. R. Sheikh, et al. Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Processing, 2004,13: 600-612
45 Z. Wang, E. P. Simoncelli, A. C. Bovik. Multi-scale structural similarity for image quality assesement. Proceedings of the 37th IEEE Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 2003: 9-12
46 R. L. Stevenson. Reduction of Coding Artifacts in Transform Image.Coding. Proc of the IEEE Trans. on Acoust,Speech,and Signal Processing, 1993,5(6):401-404
47 H. Reeve, J. Lim. Reduction of Blocking Effect in Image Coding. Proc of ICASSP’83, 1983:1212-1215
48 Ramamurthi, A. Gersho. Nonlinear Space-Variant Postprocessing of BlockCoded Images. IEEE Trans. on Acoust, Speech, Signal Processing, 1986,34(5):1258-1267
49 J. D. McDonnell, R. N. Shorten, A. D. Fagan. An Edge Classification Based Approachto the Post-Processing of Transform Encoded Images. Proc of ICASSP’94, 1994:329-332
50 B. Zeng. Reduction of Blocking Effect in DCT-Coded Images Using Zero-Masking Techniques. Signal Processing, 1999,79(2):205-211
51 Liu S Z, Bovik A C. Efficient DCT-Domain Blind Measurement and Reduction of Blocking Artifacts. IEEE Trans. on Circuits System Video Technologies, 2002,12(12): 1139-1149
52 Ying Luo, R. K. Ward. Removing the Blocking Artifacts of Block-Based DCT Compressed Images. IEEE Transactions on Image Processing, 2003,12(7):838-842
53许志良,谢胜利.一种基于人类视觉系统的去块效应算法.电子与信息学报,2005,27(11):1717-1721
54许志良,谢胜利.一种基于HVS的各向异性扩散去块效应算法.计算机工程,2006,32(2):10-12
55 N. G. Kingsbury. The Daul-tree Complex Wavelet Transform: A New Efficient Tool for Image Restoration and Enhancement, in Eusipco,1998:319-322
56周鹏,宋宇,孟晋.基于二维双树复数小波变换的图像去噪.中国西部科技,2008,7(6):36-37 44
57 D. L. Donoho. Denoising by Soft-thresholding. IEEE Transaction On Information Theory,1995,41(3):613-630
58 S. Mun, J. E. Fowler. Block compressed sensing of images using directional transforms. Proceedings of the International Conference on Image Processing, 2009: 3021-3024
59 K. Dabov, A. Foi, V. Katkovnik, et al. Image denoising with block-matching and 3D filtering. Proc. of SPIE-IS&T Electronic Imaging,2006, 606414:1-12
2 L. Zhang, W. Gao, Q.Wang, et al. Macroblock-Level Adaptive Scan Scheme for Discrete Cosine Transform Coefficients. Proc. IEEE Int. on Symp. Circuits and Systems, 2007:537-540
3 R. C. Gonzalez, R. E. Woods, S. L. Eddins.数字图像处理.阮秋琦.北京.电子工业出版社,2005:245-251
4张贤达.现代信号处理.第二版.北京:清华大学出版社,2002:378-390
5 D. F. Mix, K. J. Olejniczak.小波基础及应用教程.杨志华,杨力华.北京:机械工业出版, 2006:113-126
6 D. Taubman. High performance scalable image compression with EBCOT. IEEE Tram. on Image Processing, 2000, 9171: 1158-1170
7 C. J. Lian, K. F. Chen. H. H. Chela. Analysis and architecture design of block-coding engine for EBCOT in JPEG2000. IEEE Trans. On Circuits and Systems for Video Tchnology. 2003,13(3): 219-230
8 S. Srinivasan, C. Tu, S. L. Regunathan, et al. HD Photo: A new image coding technology for digital photography. Proc. SPIE Appl. of Digital Image Processing, 2007,6696:1-7
9 ITU-T SG16 Q.6 and ISO/IEC JTC 1/SC 29 WG1. Study Text for JPEG XR FCD (ISO/IEC 29199-2), Document N4659,2008:1-75
10 F. Dufaux, G. J. Sullivan, T. Ebrahimi. The JPEG XR Image Coding Standard. IEEE Signal Processing Magzine,2009,26(6):195-204 204-204
11 Zhang Li-bao, Wang Ke. Embedded multiple subbands scaling image coding using reversible integer wavelet transforms. Proceedings of 2004 International Symposium on Intelligent Multimedia, Video and Speech Processing, 2001,(1):201-204
12 A. R. Calderbank, I. Daubechies, W. Sweldens, et al. Lossless image compression using integer to integer wavelet transforms, Proc.IEEE ICIP, 1997,10:596-599
13 Hao Xu, Jizheng Xu, Feng Wu. Lifting-Based Directional DCT-Like Transform for Image Coding. IEEE Transactions on Circuits and Systems for Video Technology, 2001,17(10):1325-1335
14 Lei Wang, Jiaji Wu, Licheng Jiao, et al. Lossy to lossless image compression based on reversible integer DCT. 15th IEEE International Conference on Image Processing, 2008:1037-1040
15 A. Maalouf, M. C. Larabi. Low-complexity enhanced lapped transform for image coding in JPEG XR/HD Photo.16th IEEE International Conference on Image Processing (ICIP), 2009:5-8
16 H. S. Malvar. Efficient signal coding with hierarchical lapped transforms. International Conference on Acoustics, Speech, and Signal Processing, 1990,3: 1519-1522
17 Jizheng Xu, Feng Wu, Jie Liang, et al. Directional Lapped Transforms for Image Coding. Proc. IEEE Transactions on Image Processing, 2010,19:85-97
18 A. A. Skodras, A. N. Skodras. Compression of confocal microscopy images: a comparative study. Proc. of SPIE, 2008, 7008I:1-8
19 F. D. Simone, M. Ouaret, F. Dufaux, A. G. Tescher. A comparative study of JPEG2000, AVC/H.264, and HD photo. Proc. SPIE, 2007, 669602:1-11
20 Microsoft Corp.. HD Photo Specification and HD Photo Device Porting Kit 1.0, http://www.microsoft.com/windows/windowsmedia/forpros/wmphoto/, 2006
21 H. C. Reeve, J. S. Lim. Reduction of blocking effect in image coding. Proc.ICASSP Boston, 1983:1212-1215
22 T. D. Tran, Jie Liang, Chengjie Tu. Lapped Transform via Time-Domain Pre- and Post-Filtering. IEEE transaction on signal processing, 2003,51(6):1557-1571
23 H. S. Malvar, D. H. Staelin. The LOT: transform coding without blocking effects. IEEE Trans. on Acoustics Speech, and Signal Processing, 1989,37:553-559
24 H. S. Malvar. Biorthogonal and nonuniform lapped transforms for transform codingwith reduced blocking and ringing artifacts. IEEE Transaction Signal Processing, 1998:1043-1053
25 Bill Crow’s HD Photo Blog: http://blogs.msdn.com/billcrow/default.aspx,2007
26 S. H. Groder, K. W. Hsu. Design methodolgy for HD Photo compression algorithm targeting a FPGA. 2008 IEEE International SOC Conference, 2008:105-108
27 C. C. Juan, J. B. Michael, C.S. Eagle. Vulnerability Analysis of HD Photo Image Viewer Applications. Second International Conference on Secure System Integration and Reliability Improvement, 2008:1-7 14-17
28 H. S. Malvar, G. J. Sullivan, S. Srinivasan. Lifting-based reversible color transforma- tions for image compression. Proc. SPIE, 2008, 707307:1-10
29 C. J. Tu, S. Srinivasan, G. J. Sullivan. Low-complexity hierarchical lapped transform for lossy-to-lossless image coding in JPEG XR/HD Photo. Proc. of SPIE. 2008, 70730C:1-12
30 S. Srinivasan, Z. Zhou, G. J. Sullivan, et al. Coding of High Dynamic Range Images in JPEG XR/HD Photo. Proc. of SPIE, 2008, 707315:1-9
31 D. Schonberg, S .J. Sun, G. J. Sullivan. Techniques for enhancing JPEG XR/HD Photo rate-distortion performance for particular fidelity metrics. Proc. of SPIE, 2008, 707314:1-10
32 H. Koichi, T. Hiroshi, O. Hiroyuki, et al. Architecture of photo core transform in HD photo coding system for embedded systems of various bandwidths. Proc. IEEE Asia Pacific Conf. on Circuits and Systems, 2008:1592-1595
33 T. Suzuki, M. ikehara. Realization of lossless-to-lossy image coding compatible with JPEG standard by direct-lifting of DCT-IDCT. Processing of 2010 IEEE 17th international conference on image processing, Hong Kong ,2010:26-29 389-392
34许君一,孙伟,齐旭东.矩阵Kronecker乘积及其应用.计算机辅助设计与图形学学报,2003,4(15):378-388
35 M. P. Eckert, A. P. Bradley. Perceptual quality metrics applied to still image Compression. Signal Processing Volume, 1998,3(30):177-200
36 J. L. Mannos, D. J. Sakrison. The effects of a visual fidelity criterion on the encodingof Images. IEEE Trans. Inform. Theory, 1974,IT-4:525-536
37 Watson, L. Kreslake. Measurement of visual impairment scales for digital video. Proc. SPIE-Human Vision, Visual Processing, and Digital Display,2001,4299:1-7
38 G. Ramos, S. S. Hemami. Suprathreshold wavelet coefficient quantization in complex stimuli, psychophysical evaluation and analysis, 2001,18:2385-2397
39 D. M. Chandler, S. S. Hemami. Additivity models for suprathreshold distortion in quantized wavelet-coded images. SPIE-Human Vision and Electronic Imaging VII, 2002,4662:1-11
40 A. B. Watson.Visual detection of spatial contrast patterns: evaluation of five simple models. 2000,6:12-33
41 E. P. Simoncelli. Statistical models for images: compression, restoration and synthesis. Proc. 31st Asilomar Conf. Signals, Systems and Computers, Pacific Grove, CA, 1997, 11: 673-678
42 Z. Wang, A. C. Bovik. Embedded foveation image coding. IEEE Trans. Image Processing, 2001,10:1397-1410
43 Z. Wang, A. C. Bovik. A universal image quality index. IEEE Signal Processing Letters, 2002,9:81-84
44 Z. Wang, A. C. Bovik, H. R. Sheikh, et al. Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Processing, 2004,13: 600-612
45 Z. Wang, E. P. Simoncelli, A. C. Bovik. Multi-scale structural similarity for image quality assesement. Proceedings of the 37th IEEE Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 2003: 9-12
46 R. L. Stevenson. Reduction of Coding Artifacts in Transform Image.Coding. Proc of the IEEE Trans. on Acoust,Speech,and Signal Processing, 1993,5(6):401-404
47 H. Reeve, J. Lim. Reduction of Blocking Effect in Image Coding. Proc of ICASSP’83, 1983:1212-1215
48 Ramamurthi, A. Gersho. Nonlinear Space-Variant Postprocessing of BlockCoded Images. IEEE Trans. on Acoust, Speech, Signal Processing, 1986,34(5):1258-1267
49 J. D. McDonnell, R. N. Shorten, A. D. Fagan. An Edge Classification Based Approachto the Post-Processing of Transform Encoded Images. Proc of ICASSP’94, 1994:329-332
50 B. Zeng. Reduction of Blocking Effect in DCT-Coded Images Using Zero-Masking Techniques. Signal Processing, 1999,79(2):205-211
51 Liu S Z, Bovik A C. Efficient DCT-Domain Blind Measurement and Reduction of Blocking Artifacts. IEEE Trans. on Circuits System Video Technologies, 2002,12(12): 1139-1149
52 Ying Luo, R. K. Ward. Removing the Blocking Artifacts of Block-Based DCT Compressed Images. IEEE Transactions on Image Processing, 2003,12(7):838-842
53许志良,谢胜利.一种基于人类视觉系统的去块效应算法.电子与信息学报,2005,27(11):1717-1721
54许志良,谢胜利.一种基于HVS的各向异性扩散去块效应算法.计算机工程,2006,32(2):10-12
55 N. G. Kingsbury. The Daul-tree Complex Wavelet Transform: A New Efficient Tool for Image Restoration and Enhancement, in Eusipco,1998:319-322
56周鹏,宋宇,孟晋.基于二维双树复数小波变换的图像去噪.中国西部科技,2008,7(6):36-37 44
57 D. L. Donoho. Denoising by Soft-thresholding. IEEE Transaction On Information Theory,1995,41(3):613-630
58 S. Mun, J. E. Fowler. Block compressed sensing of images using directional transforms. Proceedings of the International Conference on Image Processing, 2009: 3021-3024
59 K. Dabov, A. Foi, V. Katkovnik, et al. Image denoising with block-matching and 3D filtering. Proc. of SPIE-IS&T Electronic Imaging,2006, 606414:1-12