基于三维稀疏变换的压缩传感视频重构算法研究
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摘要
当今数字视频已经渗透到商业、教育以及娱乐等各个方面,压缩传感视频重构技术成为信号处理领域一个研究热点。现有的视频重构算法大部分是基于图像重构的逐帧重构算法。这些重构算法忽略了视频的帧间相关性,存在帧间抖动现象。本文针对这些重构算法的不足,从以下几个方面进行了深入的研究:
首先,本文针对利用逐帧重构视频的不足,提出了基于三维双树复数小波和迭代收缩法的压缩传感视频重构算法。该算法利用了三维双数复数小波的多方向选择性和平移不变性,通过迭代收缩法结合可压缩性求解对应的稀疏优化问题实现视频重构。经实验仿真,该算法可以更好的恢复视频信号,消除逐帧重构产生的帧间抖动现象。
其次,本文在基于提升的运动自适应可逆变换和基于5/3滤波器的运动补偿时间滤波的基础上,提出了基于5/3运动补偿时间提升小波的压缩传感视频重构算法。该算法利用运动补偿能有效地捕捉视频中的运动信息。实验结果表明,该算法能够有效地保留视频的运动信息,消除帧间抖动现象,改善重构视频的质量。
最后,本文利用Surfacelet变换的性质,提出了基于Surfacelet变换的压缩传感视频重构算法。该算法充分利用了Surfacelet变换方向性多尺度分解特性能够有效地捕捉视频信号中的曲面奇异的特点,去除了逐帧视频重构帧间的不连续现象。实验仿真表明该算法可以在较大程度上改善重构视频的视觉效果,提高重构质量。
Today, digital video has been widely applied in many areas, such as business, education and entertainment etc. Video compressed sensing reconstruction is a research focus in communication. At present, most existing video reconstruction algorithms reconstruct video frame by frame based on image reconstruction algorithms. These algorithms ignore the coherence between video frames and exist the phenomenon of inter-frame jitter. This paper, aimed at the disadvantage of these algorithms refered above, makes some research from the follow aspects.
First of all, aiming to overcome the shortcomings of reconstruction algorithms frame by frame, we put forward a video reconstruction algorithm based on the 3D dual tree complex wavelet and iterative shrinkage. The algorithm makes full use of multidirection selectivity and translation invariance characteristics of the 3D dual tree complex wavelet, implement video reconstruction through solving corresponding optimization problem with iterative shringkage method combined with compressibility. The experiment results show that the algorithm can better recover the video signal and eliminate phenomenon of inter-frame jitter.
Secondly, a video reconstruction algorithm based on 5/3 motion-compensated temporal lifting wavelet is proposed according to lifting-based invertible motion adaptive transform and motion-compensated temporal filter based on 5/3 filter. This algorithm can effectively captures motion information using motion estimation and compensation. Experimental results show that the algorithm can effectively reserve motion information in video, eliminate inter-frame jitter and improve the quality of reconstructed video.
At last, this paper proposes a new algorithm named video reconstruction algorithm based on surfacelet transform using the nature of surfacelet transform. The algorithm makes use of multscale direction decomposition of surfacelet transform to effectively capture singularities lying on smooth surfaces and eliminates the inter-frame discontinuous of video reconstruced frame by frame. Experiments and simulations show that the algorithm can improve the visual effect and the quality of the reconstructed video.
首先,本文针对利用逐帧重构视频的不足,提出了基于三维双树复数小波和迭代收缩法的压缩传感视频重构算法。该算法利用了三维双数复数小波的多方向选择性和平移不变性,通过迭代收缩法结合可压缩性求解对应的稀疏优化问题实现视频重构。经实验仿真,该算法可以更好的恢复视频信号,消除逐帧重构产生的帧间抖动现象。
其次,本文在基于提升的运动自适应可逆变换和基于5/3滤波器的运动补偿时间滤波的基础上,提出了基于5/3运动补偿时间提升小波的压缩传感视频重构算法。该算法利用运动补偿能有效地捕捉视频中的运动信息。实验结果表明,该算法能够有效地保留视频的运动信息,消除帧间抖动现象,改善重构视频的质量。
最后,本文利用Surfacelet变换的性质,提出了基于Surfacelet变换的压缩传感视频重构算法。该算法充分利用了Surfacelet变换方向性多尺度分解特性能够有效地捕捉视频信号中的曲面奇异的特点,去除了逐帧视频重构帧间的不连续现象。实验仿真表明该算法可以在较大程度上改善重构视频的视觉效果,提高重构质量。
Today, digital video has been widely applied in many areas, such as business, education and entertainment etc. Video compressed sensing reconstruction is a research focus in communication. At present, most existing video reconstruction algorithms reconstruct video frame by frame based on image reconstruction algorithms. These algorithms ignore the coherence between video frames and exist the phenomenon of inter-frame jitter. This paper, aimed at the disadvantage of these algorithms refered above, makes some research from the follow aspects.
First of all, aiming to overcome the shortcomings of reconstruction algorithms frame by frame, we put forward a video reconstruction algorithm based on the 3D dual tree complex wavelet and iterative shrinkage. The algorithm makes full use of multidirection selectivity and translation invariance characteristics of the 3D dual tree complex wavelet, implement video reconstruction through solving corresponding optimization problem with iterative shringkage method combined with compressibility. The experiment results show that the algorithm can better recover the video signal and eliminate phenomenon of inter-frame jitter.
Secondly, a video reconstruction algorithm based on 5/3 motion-compensated temporal lifting wavelet is proposed according to lifting-based invertible motion adaptive transform and motion-compensated temporal filter based on 5/3 filter. This algorithm can effectively captures motion information using motion estimation and compensation. Experimental results show that the algorithm can effectively reserve motion information in video, eliminate inter-frame jitter and improve the quality of reconstructed video.
At last, this paper proposes a new algorithm named video reconstruction algorithm based on surfacelet transform using the nature of surfacelet transform. The algorithm makes use of multscale direction decomposition of surfacelet transform to effectively capture singularities lying on smooth surfaces and eliminates the inter-frame discontinuous of video reconstruced frame by frame. Experiments and simulations show that the algorithm can improve the visual effect and the quality of the reconstructed video.
引文
1 S. mallat.信号处理的小波导引.杨力华,戴道清,黄文良,等.第二版.北京:机械工业出版社, 2002:122-237
2 E. Candès. Ridgelets: Theory and application. Department of Statistics of Standford University, PhD Thesis, 1998:13-56
3 E. Candès, D. Donoho. Curvelets-A Surprising Effective Nonadaptive Represenstion for Objects with edges. Curves and Surfcaces, Vanderbilt University Press, Nashvielle TN, 2000:105-120
4 E. L. Pennec, S. Mallat. Image Compression with Geometrical wavelets. International Conference of Image Processing, Vancouver, Canada, 2000:661-664
5 M. N. Do, M. Vetterli. The Contourlet Transform: An Efficient Directional Multiresolution Image Representation. IEEE Transaction on Image Processing, 2005, 14(12):2091-2106
6 N. G. Kingsbury. The Dual-tree Complex Wavelet Transform: A New Efficient Tool for Image Restoration and Enhancement. In Proc. European Signal Processing Conference, Rhodes, 1998:319-322
7 I. W. Selesnick, L. Sendur. Video denoising using 2D and 3D dual-tree complex wavelet transforms. Wavelet: Applications in Signal and Image Processing X, Proceedings of the SPIE Conf, 2003:607-618
8 E. Candès, J. Romberg. T. Tao. Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information. IEEE Transactions on Information Theory, 2006, 52(2):489-509
9 E. Candès, T. Tao. Near Optimal Signal Recovery from Random Projections: Universal Encoding Strategies? IEEE Transaction on Information Theory, 2006, 52(12): 5406-5424
10 D. L. Donoho. Compressed Sensing. IEEE Transactions on Information Theory, 2006,52(4):1289-1306
11 E. Candès. Compressed Sampling. Proc.of International Congress of Mathematics, Madrid, Spain, 2006, 3:1433-1452
12 E. Candès, T. Tao. Decoding by Linear Programming. IEEE Transaction on Information Theory, 2005, 51(12):4203-4215
13 R. Coifman, F. Geshwind, Y. Meyer. Noiselets, Applied and Communicational Harmonic Analysis. 2001, 10(1):27-44
14 Richard Baraniuk. Compressive Imaging: A new framework for computational image processing. 2006: http: //dsp. ece.rice.edu/~richb/talks
15 E. Candès, J. Romberg. Sparsity and Incoherence in Compressive Sampling. Inverse Problems, 2007, 23(3):969-985
16 Lu Gan, Thong Do, T. D.Tran. Fast Compressive Imaging Using Scrambled Block Hadamard Ensemble. 2008:http://www.dsp.ece.rice.edu/cs/ scrambled_blk_ WHT.pdf
17 T. T. Do., T.D.Tran., Lu Gan. Fast Compressive Sampling with Structurally Rrandom Matrices. IEEE International Conference on Acoustics Speech and Signal Processing. 2008, 4:3369-3372
18方红,章权兵,韦穗.基于非常稀疏随机投影的重建方法.计算机工程与应用, 2007, 43(22):25-27
19 E. J. Candès, M. B. Wakin. An Introduction to Compressive Sampling. IEEE Signal Processing Magazine, 2008, 25(2):21-30
20 S. G. Mallat, Z. Zhang. Matching Pursuits with Time-frequency Dictionaries. IEEE Transactions on Signal Processing, 1993:3397-3415
21 J. Tropp, A. Gilbert. Signal Recovery from Random Measurements via Orthogonal Matching Pursuit. IEEE Trans. on Information Theory, 2007, 53(12):4655-4666
22 D. L. Donoho, Y. Tsaig, I.Drori, et al. Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit. Tech. Report, Department of statistics, Standford university, 2006:5-10
23 S. S. Chen, D. L. Donoho, M. A. Saunders. Atomic Decomposition by Basis Pursuit. SIAMJ. Sci. Comput., 1998, 20(1):36-61
24 Seung-jean Kim, Kwangmoo Koh, Micheal Lustig, et al. An Efficient Method for Compressed Sensing. IEEE International Conference on Imgae Processing,San Antonio, 2007, 3:117-120
25 E. J. Candes, J. Romberg. Practical Signal Recovery from Random Projections. In: Proceedings of SPIE Computational Imaging III, San Jose, 2005:76-86
26 I. Daubechies, M. Defrise, C. D. Mol. An Iterative Thresholding Algorithm for Linear Inverse Problems with A Sparsity Constraint. Communications on Pure and Applied Mathematics, 2004, 57(11):1413-1457
27 J. M. Bioucas-Dias, M. A.T.Figueiredo. Two-step Algorithms for Linear Inverse Problems with Non-quadratic Regularization. Proceeding of ICIP, IEEE International Conference on Image Processing, San Antonio, 2007, 1:I-105-I-108
28 M. Elad, B. Matalon, J. Shtok. A Wide-angle View at Iterated Shrinkage Algorithms. 2007:http://www.cs.technion.ac.il/~elad/publications/conferences/2007/Iterated_Shrinkage_SPIE_2007.pdf
29 S. S. Chen, D. L. Donoho, M. A. Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 1999, 20(1):33-61
30 M. Figueiredo, R. Nowak, S. Wright. Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems. IEEE Selected topics in signal processing. 2007, 1(4):586-597
31 D. Needell, R. Vershynin. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. Foundations of Computational Mathematics, 2009, 6(9):317-334
32 R. Chartand, Wotao Tin. Iterativelty Reweighted Algorithm for Compressive Sensing. IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas, 2008:3869-3872
33 W. Yin, S. Osher, D. Goldfarb, et al. Bregman Iterative Algorithms for L1-minimization with Applications to Compressed Sensing. SIAM J. Imaging Science, 2008, 1(1):143-168
34 M. F. Duarte, M. A. Davenport, D. Takhar, et al. Single-pixel Imaging via CompressiveSampling. IEEE Siganl Processing Magazine. 2008, 25(2):83-91
35 D. Takhar, V. Bansal, M. Wakin, et al. A Compressed Sensing Camera: New Theory and An Implementation Using Digital Micromirrors. Tech. Reprot, Proc. Comp. Imaging IV at SPIE Electronic Imaging, San Jose, California, 2006:3-7
36 M. Lustig, D. Donoho, J. M. Pauly. Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging. Magnetic Resonance in Medicine, 2007, 58(6):1182-1195
37 S. Hu, M. Lustig, Albert P.Chen, et al. Compressed Sensing for Resolution Enhancement of Hyperpolarized 13C Flyback 3D-MRSI. Journal of Magnetic Resonance, 2008, 92(2):258-264
38 R. Baraniuk, P. Steeghs. Compressive Radar Imaging. IEEE Radar Conference, Waltham, Massachusetts, 2007:128-133
39 L. Potter, P. Schniter, J. Ziniel. Sparse Reconstruction for Radar. SPIE Algorithms for Synthetic Aperture Radar Imagery XV, 2008, (6970):69703
40 J. Laska, S. Kirolos, M. Duarte, et al. Theory and Implementation of An Analog-to-information Converter Using Random Demodulation. IEEE Int. Symp. on Circuits and Systems (ISCAS), New Orleans, Louisiana, 2007:1959-1962
41 Georg Taub?ck, Franz Hlawatsch. A Compressed Sensing Technique for OFDM Channel Estimation in Mobile Environments: Exploiting Channel Sparsity for Reducing Pilots. IEEE International Conference on Acoustics, Speech, and Signal Processing, Las Vegas, Nevada, 2008:2885-2888
42 W. U. Bajwa, J. Haupt, G. Raz, et al. Compressed Channel Sensing. Proc.of Conference on Infomation Sciences and Systems (CISS), Princeton, New Jersey, 2008:5-10
43 S. F. Cotter, B. D. Rao. Sparse Channel Estimation via Matching Pursuit with Application to Equalization. IEEE Trans. on Communications, 2002, 50(3):374-377
44 Mona Sheikh, Olgica Milenkovic, Richard Baraniuk. Compressed Sensing DNA Microarrys. 2007:http://www.ece.rice.edu/~msheikh/csm_techrep2.pdf
45 G. Hennenfent, F. J. Herrmann. Simply Denoise: Wavefield Reconstruction via JitteredUndersampling. Geophysics, 2008, 73(3):V19-V28
46 J. Bobin, J.L.Starck, R. Ottensamer. Compressed Sensing in Astronomy. IEEE Journal of Selected Topics in Signal Processing, 2008, 2(5):718-726
47 Jianwei Ma. Single-pixel Remote Sensing. IEEE Geoscience and Romote Sensing Letters, 2009, 6(2):199-203
48 P. Borgnant, P. Flandrin. Time Frequency Localization from Sparsity Constrains. IEEE International Conference on Acoustics Speech and Signal Processing,2008:3785-3788
49 D. L. Donoho, X. Huo. Uncertainty Principles and Ideal Atomic Decomposition. IEEE Trans. Inform. Theory, 2001, 47(7):2845-2862
50 D. S. Taubman, M. W. Marcellin. JPEG 2000: Image Compression Fundamentals, Standards and Practice. Kluwer International Series in Engineering and Computer Science, 2002, 11:20-63
51 H. Rauhut, K. Schass, P. Vandergheynst. Compressed Sensing and Redundant Dictionaries. IEEE Trans. on Information Theory, 2008, 54(5):2210-2219
52 M. Lustig, J. M. Santos, D. L. Donoho, et al. K-t SPARSE: High Frame Rate Dynamic MRI Exploiting Spatio-temporal Sparsity. ISMRM, Seattle, Washington, 2006:2420-2431
53 E. J. Candès, J. Romberg, T. Tao. Stable Signal Recovery from Incomplete and Inaccurate Measurements. Communication on Pure and Applied Mathematics, 2006, 59(8):1207-1233
54 Richard Baraniuk, Volkan Cevher, Marco Duarte, et al. Model-Based Compressive Sensing. 2008: http://arxiv.org/PS_cache/arxiv/pdf/0808/0808.3572v2.pdf
55 Y. M. Lu, M. N. Do. Multidimensional directional Filter Banks and Surfacelets. IEEE Transactions on Image Processing, 2007, 16(4):918-931
56 L. I. Rudin, S. Osher, E. Fatemi. Nonlinear Total Variation Based Noise Removal Algorithms. Physica D, 1992, 60(1-4):259-268
57 I. W. Selesnick, R. G. Baraniuk, N. G. Kingsbury. The Dual Tree Complex Wavelet Transform. IEEE Signal Processing Magazine, 2005, 22(6):123-151
58 N. G. Kingsbury. Complex Wavelet for Shift Invariant Analysis and Filtering ofSignals. Applied and Computational Harmonic Analysis, 2001, 10(3):234-253
59 L. W. Kang, C. S. Lu. Distributed compressive video sensing. Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, Washington DC. USA, 2009:1169-1172
60 Andrew Secker, David Taubman. Lifting-based Invertible Motion Adaptive Transform(LIMAT) Framework for Highly Scalable Video Compression.IEEE Transactions on Image Processing, 2003, 12(12):1530-1542
61 J. R. Ohm. Three-dimensional Subband Coding with Motion Compensation.IEEE Trans. on Image Processing, 1994, 3(5):559-571
62 S. J. Choi, J. W.Woods. Motion-compensated 3-D Subband Coding of Video.IEEE Trans. on Image Processing, 1999, 8(2):155-167
63 Sweldensw. The lifting scheme: A new philosophy in biorthogonal wavelet constructions. Proceedings of SPIE on Wavelet Applications in Signal and Image Processing III. San Diego: SPIE, 1995:68-79
64 I. I. Daubech, Sweldensw. Factoring wavelet transforms into lifting steps.Journal of Fourier Analysis and Application, 1998, 4(3):247-269
65 D. Le Gall, A. Tabatabai. Subband coding of digital images using symmetric short kernel filters and arithmetic coding techniques. IEEE International Conference on Acoustics, Speech and Signal Processing. 1988, 2:761-764
66夏超,冯燕.一种基于H.264的快速帧间预测算法.微计算机应用,2007,28(10):1024-1028
67 H. Kalva. The H.264 Video Coding Standard. IEEE Multimedia, 2006, 13(4):86-90.
68 P. Yin. Fast Mode Decision and Motion Estimation for JVT/H.264. IEEE international Conference on Multimedia&Expo Maryland, 2003:853-856
69 R. H. Bamberger, M. J. T. Smith. A filter bank for the directional decomposition of images: Theory and design. IEEE Trans. Signal Process. 1992, 40(4): 882-893
70闫敬文,屈小波.超小波分析及应用.第一版.北京:国防工业出版社, 2008:33-45
2 E. Candès. Ridgelets: Theory and application. Department of Statistics of Standford University, PhD Thesis, 1998:13-56
3 E. Candès, D. Donoho. Curvelets-A Surprising Effective Nonadaptive Represenstion for Objects with edges. Curves and Surfcaces, Vanderbilt University Press, Nashvielle TN, 2000:105-120
4 E. L. Pennec, S. Mallat. Image Compression with Geometrical wavelets. International Conference of Image Processing, Vancouver, Canada, 2000:661-664
5 M. N. Do, M. Vetterli. The Contourlet Transform: An Efficient Directional Multiresolution Image Representation. IEEE Transaction on Image Processing, 2005, 14(12):2091-2106
6 N. G. Kingsbury. The Dual-tree Complex Wavelet Transform: A New Efficient Tool for Image Restoration and Enhancement. In Proc. European Signal Processing Conference, Rhodes, 1998:319-322
7 I. W. Selesnick, L. Sendur. Video denoising using 2D and 3D dual-tree complex wavelet transforms. Wavelet: Applications in Signal and Image Processing X, Proceedings of the SPIE Conf, 2003:607-618
8 E. Candès, J. Romberg. T. Tao. Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information. IEEE Transactions on Information Theory, 2006, 52(2):489-509
9 E. Candès, T. Tao. Near Optimal Signal Recovery from Random Projections: Universal Encoding Strategies? IEEE Transaction on Information Theory, 2006, 52(12): 5406-5424
10 D. L. Donoho. Compressed Sensing. IEEE Transactions on Information Theory, 2006,52(4):1289-1306
11 E. Candès. Compressed Sampling. Proc.of International Congress of Mathematics, Madrid, Spain, 2006, 3:1433-1452
12 E. Candès, T. Tao. Decoding by Linear Programming. IEEE Transaction on Information Theory, 2005, 51(12):4203-4215
13 R. Coifman, F. Geshwind, Y. Meyer. Noiselets, Applied and Communicational Harmonic Analysis. 2001, 10(1):27-44
14 Richard Baraniuk. Compressive Imaging: A new framework for computational image processing. 2006: http: //dsp. ece.rice.edu/~richb/talks
15 E. Candès, J. Romberg. Sparsity and Incoherence in Compressive Sampling. Inverse Problems, 2007, 23(3):969-985
16 Lu Gan, Thong Do, T. D.Tran. Fast Compressive Imaging Using Scrambled Block Hadamard Ensemble. 2008:http://www.dsp.ece.rice.edu/cs/ scrambled_blk_ WHT.pdf
17 T. T. Do., T.D.Tran., Lu Gan. Fast Compressive Sampling with Structurally Rrandom Matrices. IEEE International Conference on Acoustics Speech and Signal Processing. 2008, 4:3369-3372
18方红,章权兵,韦穗.基于非常稀疏随机投影的重建方法.计算机工程与应用, 2007, 43(22):25-27
19 E. J. Candès, M. B. Wakin. An Introduction to Compressive Sampling. IEEE Signal Processing Magazine, 2008, 25(2):21-30
20 S. G. Mallat, Z. Zhang. Matching Pursuits with Time-frequency Dictionaries. IEEE Transactions on Signal Processing, 1993:3397-3415
21 J. Tropp, A. Gilbert. Signal Recovery from Random Measurements via Orthogonal Matching Pursuit. IEEE Trans. on Information Theory, 2007, 53(12):4655-4666
22 D. L. Donoho, Y. Tsaig, I.Drori, et al. Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit. Tech. Report, Department of statistics, Standford university, 2006:5-10
23 S. S. Chen, D. L. Donoho, M. A. Saunders. Atomic Decomposition by Basis Pursuit. SIAMJ. Sci. Comput., 1998, 20(1):36-61
24 Seung-jean Kim, Kwangmoo Koh, Micheal Lustig, et al. An Efficient Method for Compressed Sensing. IEEE International Conference on Imgae Processing,San Antonio, 2007, 3:117-120
25 E. J. Candes, J. Romberg. Practical Signal Recovery from Random Projections. In: Proceedings of SPIE Computational Imaging III, San Jose, 2005:76-86
26 I. Daubechies, M. Defrise, C. D. Mol. An Iterative Thresholding Algorithm for Linear Inverse Problems with A Sparsity Constraint. Communications on Pure and Applied Mathematics, 2004, 57(11):1413-1457
27 J. M. Bioucas-Dias, M. A.T.Figueiredo. Two-step Algorithms for Linear Inverse Problems with Non-quadratic Regularization. Proceeding of ICIP, IEEE International Conference on Image Processing, San Antonio, 2007, 1:I-105-I-108
28 M. Elad, B. Matalon, J. Shtok. A Wide-angle View at Iterated Shrinkage Algorithms. 2007:http://www.cs.technion.ac.il/~elad/publications/conferences/2007/Iterated_Shrinkage_SPIE_2007.pdf
29 S. S. Chen, D. L. Donoho, M. A. Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 1999, 20(1):33-61
30 M. Figueiredo, R. Nowak, S. Wright. Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems. IEEE Selected topics in signal processing. 2007, 1(4):586-597
31 D. Needell, R. Vershynin. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. Foundations of Computational Mathematics, 2009, 6(9):317-334
32 R. Chartand, Wotao Tin. Iterativelty Reweighted Algorithm for Compressive Sensing. IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas, 2008:3869-3872
33 W. Yin, S. Osher, D. Goldfarb, et al. Bregman Iterative Algorithms for L1-minimization with Applications to Compressed Sensing. SIAM J. Imaging Science, 2008, 1(1):143-168
34 M. F. Duarte, M. A. Davenport, D. Takhar, et al. Single-pixel Imaging via CompressiveSampling. IEEE Siganl Processing Magazine. 2008, 25(2):83-91
35 D. Takhar, V. Bansal, M. Wakin, et al. A Compressed Sensing Camera: New Theory and An Implementation Using Digital Micromirrors. Tech. Reprot, Proc. Comp. Imaging IV at SPIE Electronic Imaging, San Jose, California, 2006:3-7
36 M. Lustig, D. Donoho, J. M. Pauly. Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging. Magnetic Resonance in Medicine, 2007, 58(6):1182-1195
37 S. Hu, M. Lustig, Albert P.Chen, et al. Compressed Sensing for Resolution Enhancement of Hyperpolarized 13C Flyback 3D-MRSI. Journal of Magnetic Resonance, 2008, 92(2):258-264
38 R. Baraniuk, P. Steeghs. Compressive Radar Imaging. IEEE Radar Conference, Waltham, Massachusetts, 2007:128-133
39 L. Potter, P. Schniter, J. Ziniel. Sparse Reconstruction for Radar. SPIE Algorithms for Synthetic Aperture Radar Imagery XV, 2008, (6970):69703
40 J. Laska, S. Kirolos, M. Duarte, et al. Theory and Implementation of An Analog-to-information Converter Using Random Demodulation. IEEE Int. Symp. on Circuits and Systems (ISCAS), New Orleans, Louisiana, 2007:1959-1962
41 Georg Taub?ck, Franz Hlawatsch. A Compressed Sensing Technique for OFDM Channel Estimation in Mobile Environments: Exploiting Channel Sparsity for Reducing Pilots. IEEE International Conference on Acoustics, Speech, and Signal Processing, Las Vegas, Nevada, 2008:2885-2888
42 W. U. Bajwa, J. Haupt, G. Raz, et al. Compressed Channel Sensing. Proc.of Conference on Infomation Sciences and Systems (CISS), Princeton, New Jersey, 2008:5-10
43 S. F. Cotter, B. D. Rao. Sparse Channel Estimation via Matching Pursuit with Application to Equalization. IEEE Trans. on Communications, 2002, 50(3):374-377
44 Mona Sheikh, Olgica Milenkovic, Richard Baraniuk. Compressed Sensing DNA Microarrys. 2007:http://www.ece.rice.edu/~msheikh/csm_techrep2.pdf
45 G. Hennenfent, F. J. Herrmann. Simply Denoise: Wavefield Reconstruction via JitteredUndersampling. Geophysics, 2008, 73(3):V19-V28
46 J. Bobin, J.L.Starck, R. Ottensamer. Compressed Sensing in Astronomy. IEEE Journal of Selected Topics in Signal Processing, 2008, 2(5):718-726
47 Jianwei Ma. Single-pixel Remote Sensing. IEEE Geoscience and Romote Sensing Letters, 2009, 6(2):199-203
48 P. Borgnant, P. Flandrin. Time Frequency Localization from Sparsity Constrains. IEEE International Conference on Acoustics Speech and Signal Processing,2008:3785-3788
49 D. L. Donoho, X. Huo. Uncertainty Principles and Ideal Atomic Decomposition. IEEE Trans. Inform. Theory, 2001, 47(7):2845-2862
50 D. S. Taubman, M. W. Marcellin. JPEG 2000: Image Compression Fundamentals, Standards and Practice. Kluwer International Series in Engineering and Computer Science, 2002, 11:20-63
51 H. Rauhut, K. Schass, P. Vandergheynst. Compressed Sensing and Redundant Dictionaries. IEEE Trans. on Information Theory, 2008, 54(5):2210-2219
52 M. Lustig, J. M. Santos, D. L. Donoho, et al. K-t SPARSE: High Frame Rate Dynamic MRI Exploiting Spatio-temporal Sparsity. ISMRM, Seattle, Washington, 2006:2420-2431
53 E. J. Candès, J. Romberg, T. Tao. Stable Signal Recovery from Incomplete and Inaccurate Measurements. Communication on Pure and Applied Mathematics, 2006, 59(8):1207-1233
54 Richard Baraniuk, Volkan Cevher, Marco Duarte, et al. Model-Based Compressive Sensing. 2008: http://arxiv.org/PS_cache/arxiv/pdf/0808/0808.3572v2.pdf
55 Y. M. Lu, M. N. Do. Multidimensional directional Filter Banks and Surfacelets. IEEE Transactions on Image Processing, 2007, 16(4):918-931
56 L. I. Rudin, S. Osher, E. Fatemi. Nonlinear Total Variation Based Noise Removal Algorithms. Physica D, 1992, 60(1-4):259-268
57 I. W. Selesnick, R. G. Baraniuk, N. G. Kingsbury. The Dual Tree Complex Wavelet Transform. IEEE Signal Processing Magazine, 2005, 22(6):123-151
58 N. G. Kingsbury. Complex Wavelet for Shift Invariant Analysis and Filtering ofSignals. Applied and Computational Harmonic Analysis, 2001, 10(3):234-253
59 L. W. Kang, C. S. Lu. Distributed compressive video sensing. Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, Washington DC. USA, 2009:1169-1172
60 Andrew Secker, David Taubman. Lifting-based Invertible Motion Adaptive Transform(LIMAT) Framework for Highly Scalable Video Compression.IEEE Transactions on Image Processing, 2003, 12(12):1530-1542
61 J. R. Ohm. Three-dimensional Subband Coding with Motion Compensation.IEEE Trans. on Image Processing, 1994, 3(5):559-571
62 S. J. Choi, J. W.Woods. Motion-compensated 3-D Subband Coding of Video.IEEE Trans. on Image Processing, 1999, 8(2):155-167
63 Sweldensw. The lifting scheme: A new philosophy in biorthogonal wavelet constructions. Proceedings of SPIE on Wavelet Applications in Signal and Image Processing III. San Diego: SPIE, 1995:68-79
64 I. I. Daubech, Sweldensw. Factoring wavelet transforms into lifting steps.Journal of Fourier Analysis and Application, 1998, 4(3):247-269
65 D. Le Gall, A. Tabatabai. Subband coding of digital images using symmetric short kernel filters and arithmetic coding techniques. IEEE International Conference on Acoustics, Speech and Signal Processing. 1988, 2:761-764
66夏超,冯燕.一种基于H.264的快速帧间预测算法.微计算机应用,2007,28(10):1024-1028
67 H. Kalva. The H.264 Video Coding Standard. IEEE Multimedia, 2006, 13(4):86-90.
68 P. Yin. Fast Mode Decision and Motion Estimation for JVT/H.264. IEEE international Conference on Multimedia&Expo Maryland, 2003:853-856
69 R. H. Bamberger, M. J. T. Smith. A filter bank for the directional decomposition of images: Theory and design. IEEE Trans. Signal Process. 1992, 40(4): 882-893
70闫敬文,屈小波.超小波分析及应用.第一版.北京:国防工业出版社, 2008:33-45