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压缩感知及其图像处理应用研究进展与展望

任越美 张艳宁 李映

任越美, 张艳宁, 李映. 压缩感知及其图像处理应用研究进展与展望. 自动化学报, 2014, 40(8): 1563-1575. doi: 10.3724/SP.J.1004.2014.01563
引用本文: 任越美, 张艳宁, 李映. 压缩感知及其图像处理应用研究进展与展望. 自动化学报, 2014, 40(8): 1563-1575. doi: 10.3724/SP.J.1004.2014.01563
REN Yue-Mei, ZHANG Yan-Ning, LI Ying. Advances and Perspective on Compressed Sensing and Application on Image Processing. ACTA AUTOMATICA SINICA, 2014, 40(8): 1563-1575. doi: 10.3724/SP.J.1004.2014.01563
Citation: REN Yue-Mei, ZHANG Yan-Ning, LI Ying. Advances and Perspective on Compressed Sensing and Application on Image Processing. ACTA AUTOMATICA SINICA, 2014, 40(8): 1563-1575. doi: 10.3724/SP.J.1004.2014.01563

压缩感知及其图像处理应用研究进展与展望

doi: 10.3724/SP.J.1004.2014.01563
基金项目: 

国家自然科学基金(61231016,61301192,61272288,61201291),河南省科技攻关计划(142102210557),西北工业大学基础研究基金(JCT20130108,JC201120,JC201148)资助

详细信息
    作者简介:

    张艳宁 西北工业大学计算机学院教授.主要研究方向为智能信息处理与视频分析技术.E-mail:ynzhang@nwpu.edu.cn

Advances and Perspective on Compressed Sensing and Application on Image Processing

Funds: 

Supported by National Natural Science Foundation of China (61231016, 61301192, 61272288, 61201291), Key Science and Technology Program of Henan Province (142102210557), NPU Foundation for Fundamental Research (JCT20130108, JC201120, JC201148)

  • 摘要: 压缩感知理论(Compressed sensing,CS)通过少量的线性测量值感知信号的原始结构,并通过求解最优化问题精确地重构原信号.该理论减少了数字图像及视频 获取时的存储及传输代价,也为后续的图像处理及识别的研究提供了新的契机,促进了理论和工程应用的结合. 阐述了CS的基本原理,综述了其关键技术稀疏变换、观测矩阵 设计、重构算法的一系列最新理论成果和发展,深入分析和比较了CS理论应用到图像处理领域的研究和发展状况,总结了其中存在的问题,并对未来的应用前景进行了展望.
  • [1] Candes E J, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 2006, 52(2): 489-509
    [2] [2] Donoho, D L. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306
    [3] Li Shu-Tao, Wei Dan. A survey on compressive sensing. Acta Automatica Sinica, 2009, 35(11): 1369-1377(李树涛, 魏丹. 压缩传感综述. 自动化学报, 2009, 35(11): 1369-1377)
    [4] Dai Qiong-Hai, Fu Chang-Jun, Ji Xiang-Yang. Research on compressed sensing. Chinese Journal of Computers, 2011, 34(3): 425-434 (戴琼海, 付长军, 季向阳. 压缩感知研究. 计算机学报, 2011, 34(3): 425-434)
    [5] Shi Guang-Ming, Liu Dan-Hua, Gao Da-Hua, Liu Zhe, Lin Jie, Wang Liang-Jun. Advances in theory and application of compressed sensing. Acta Electronica Sinica, 2009, 37(5): 1071-1081(石光明, 刘丹华, 高大化, 刘哲, 林杰, 王良君. 压缩感知理论及其研究进展. 电子学报, 2009, 37(5): 1071-1081)
    [6] Jiao Li-Cheng, Yang Shu-Yuan, Liu Fang, Hou Biao. Devel-opment and prospect of compressive sensing. Acta Electronica Sinica, 2011, 39(7): 1651-1662(焦李成, 杨淑媛, 刘芳, 侯彪. 压缩感知回顾与展望. 电子学报, 2011, 39(7): 1651-1662)
    [7] Liu Fang, Wu Jiao, Yang Shu-Yuan, Jiao Li-Cheng. Research advances on structured compressive sensing. Acta Automatica Sinica, 2013, 39(12): 1980-1995(刘芳, 武娇, 杨淑媛, 焦李成. 结构化压缩感知研究进展. 自动化学报, 2013, 39(12): 1980-1995)
    [8] [8] Duarte M F, Sarvotham S, Baron D, Wakin M B, Baraniuk R G. Distributed compressed sensing of jointly sparse signals. In: Proceedings of the 39th Asilomar Conference on Signals, Systems and Computers. Pacific Grove, California: IEEE, 2005. 1537-1541
    [9] [9] Wang W, Garofalakis M, Ramchandran K. Distributed sparse random projections for refinable approximation. In: Proceedings of the 6th International Symposium on Information Processing in Sensor Networks. Cambridge, MA: IEEE, 2007. 331-339
    [10] Ji S H, Xue Y, Carin L. Bayesian compressive sensing. IEEE Transactions on Signal Processing, 2008, 56(6): 2346-2356
    [11] Ji S H, Dunson D, Carin L. Multitask compressive sensing. IEEE Transactions on Signal Processing, 2009, 57(1): 92-106
    [12] Mallat S G. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989, 11(7): 674-693
    [13] Olshausen B A, Field D J. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 1996, 381(6583): 607-609
    [14] Candes E J. Ridgelets: Theory and Applications. Stanford: Stanford University, 1998
    [15] Candes E J, Donoho D L. Curvelets-a surprisingly effective nonadaptive representation for objects with edges. Technical Report, Department of Statistics, Stanford University, USA, 1999
    [16] Do M N, Vetterli M. The Contourlet transform: an efficient directional multiresolution image representation. IEEE Transactions on Image Processing, 2005, 14(12): 2091-2106
    [17] Figueras I, Ventura R M, Vandergheynst P, Frossard P. Low-rate and flexible image coding with redundant representations. IEEE Transactions on Image Processing, 2006, 15(3): 726-739
    [18] Yaghoobi M, Daudet L, Davies M E. Parametric dictionary design for sparse coding. IEEE Transactions on Signal Processing, 2009, 57(12): 4800-4810
    [19] Lian Qiu-Sheng, Chen Shu-Zhen. Image recontruction for compressed sensing based on the combined sparse image representation. Acta Automatica Sinica, 2010, 36(3): 385-391(练秋生, 陈书贞. 基于混合基稀疏图像表示的压缩传感图像重构. 自动化学报, 2010, 36(3): 385-391)
    [20] Peyre G. Best basis compressed sensing. IEEE Transactions on Signal Processing, 2010, 58(5): 2613-2622
    [21] Sun Yu-Bao, Xiao Liang, Wei Zhi-Hui, Shao Wen-Ze. Sparse representations of images by a multi-component Gabor perception dictionary. Acta Automatica Sinica, 2008, 34(11): 1379-1387(孙玉宝, 肖亮, 韦志辉, 邵文泽. 基于Gabor感知多成份字典的图像稀疏表示算法研究. 自动化学报, 2008, 34(11): 1379-1387)
    [22] Bryt O, Elad M. Compression of facial images using the K-SVD algorithm. Journal of Visual Communication and Image Representation, 2008, 19(4): 270-282
    [23] Mairal J, Bach F, Ponce J, Sapiro G. Online learning for matrix factorization and sparse coding. Journal of Machine Learning Research, 2010, 11: 19-60
    [24] Candes E J, Tao T. Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Transactions on Information Theory, 2006, 52(12): 5406-5425
    [25] Baraniuk R G. Compressive sensing. IEEE Signal Processing Magazine, 2007, 24(4): 118-121
    [26] Donoho D L. For most large underdetermined systems of linear equations, the minimal l1 norm near-solution approximates the sparsest near-solution. Communications on Pure and Applied Mathematics, 2006, 59(7): 907-934
    [27] Fang Hong, Zhang Quan-Bing, Wei Sui. A method of image reconstruction based on sub-Gaussian random projection. Journal of Computer Research and Development, 2008, 45(8): 1402-1407 (方红, 章权兵, 韦穗. 基于亚高斯随机投影的图像重建方法. 计算机研究与发展, 2008, 45(8): 1402-1407)
    [28] Gilbert A C, Guha S, Indyk P, Muthukishna S, Strauss M. Near-optimal sparse Fourier representations via sampling. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing. Quebec, Canada: ACM Press, 2006. 152-161
    [29] Do T T, Tran T D, Lu G. Fast compressive sampling with structurally random matrices. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing. Washington D.C., USA: IEEE, 2008. 3369-3372
    [30] Tropp J A, Gilbert A C. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory, 2007, 53(12): 4655-4666
    [31] Yin W, Morgan S, Yang J, Zhang Y. Practical compressive sensing with toeplitz and circulant matrices. In: Proceedings of SPIE-The International Society for Optical Engineering: Visual Communications and Image Processing. Huangshan, China: SPIE 2010
    [32] DeVore R A. Deterministic constructions of compressed sensing matrices. Journal of Complexity, 2007, 23(4-6): 918-925
    [33] Li X B, Zhao R Z, Hu S H. Blocked polynomial deterministic matrix for compressed sensing. In: Proceedings of the 6th International conference on wireless communications networking and mobile computing. Chengdu, China: IEEE, 2010. 1-4
    [34] Shi Q F, Li H X, Shen C H. Rapid face recognition using hashing. In: Proceedings of In Proceedings of the 2010 IEEE Conference on Computer Vision and Pattern Recognition. San Francisco, CA: IEEE, 2010. 2753-2760
    [35] Song Xiao-Xia, Shi Guang-Ming. Fewer Bernoulli measurments satisfying the constraint of reconstruction probability. Acta Automatica Sinica, 2013, 39(1): 53-56(宋晓霞, 石光明. 满足重构概率约束的更少贝努利观测. 自动化学报, 2013, 39(1): 53-56)
    [36] Needell D, Vershynin R. Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(2): 310-316
    [37] Needell D, Tropp J A. CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 2009, 26(3): 301-321
    [38] Wei D, Milenkovic O. Subspace pursuit for compressive sensing signal reconstruction. IEEE Transactions on Information Theory, 2009, 55(5): 2230-2249
    [39] Do T T, Gan L, Nguyen N, Tran T D. Sparsity adaptive matching pursuit algorithm for practical compressed sensing. In: Proceedings of the 42nd Asilomar Conference on Signals, Systems and Computers. Pacific Grove, C A: IEEE, 2008. 581-587
    [40] Liu Ya-Xin, Zhao Rui-Zhen, Hu Shao-Hai, Jiang Chun-Hui. Regularized adaptive matching pursuit algorithm for signal reconstruction based on compressive sensing. Journal of Electronics Information Technology, 2010, 32(11): 2713-2717(刘亚新, 赵瑞珍, 胡绍海, 姜春晖. 用于压缩感知信号重建的正则化自适应匹配追踪算法. 电子与信息学报, 2010, 32(11): 2713-2717)
    [41] Blumensath T, Davies M E. Stagewise weak gradient pur-suits. IEEE Transactions on Signal Processing, 2009, 57(11): 4333-4346
    [42] Li Zhi-Lin, Chen Hou-Jin, Yao Chang, Li Ju-Peng. Compressed sensing reconstruction algorithm based on spectral projected gradient pursuit. Acta Automatica Sinica, 2012, 38(7): 1218-1223(李志林, 陈后金, 姚畅, 李居朋. 基于谱投影梯度追踪的压缩感知重建算法. 自动化学报, 2012, 38(7): 1218-1223)
    [43] Fang Y. Sparse matrix recovery from random samples via 2D orthogonal matching pursuit. IEEE Transactions on Signal Processing, to be published
    [44] Candes E J, Romberg J, Tao T. Stable signal recovery from incomplete and inaccurate measurements. Communications on pure and Applied Mathematics, 2006, 59(8): 1207-1223
    [45] Csaba Mszros. Regularization techniques in interior point methods. Journal of Computational and Applied Mathematics, 2012, 236(15): 3704-3709
    [46] Blumensath T, Davies M E. Iterative hard thresholding for compressed sensing. Applied and Computational Harmonic Analysis, 2009, 27(3): 265-274
    [47] Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4): 586-597
    [48] Bioucas-Dias J M, Figueiredo M A T. A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Transactions on Image Processing, 2007, 16(12): 2992-3004
    [49] Wright S J, Nowak R D, Figueiredo M A T. Sparse reconstruction by separable approximation. IEEE Transactions on Signal Processing, 2009, 57(7): 2479-2493
    [50] Afonso M V, Bioucas-Dias J M, Figueiredo M A T. Fast image recovery using variable splitting and constrained optimization. IEEE Transactions on Image Processing, 2010, 19(9): 2345-2356
    [51] Pan H, Jing Z L, Lei M, Liu R L, Jin B, Zhang C L. A sparse proximal Newton splitting method for constrained image deblurring. Neurocomputing, 2013, 122: 245-257
    [52] Duan Y P, Huang W M. A fixed-point augmented Lagrangian method for total variation minimization problems. Journal of Visual Communication and Image Representation, 2013, 24(7): 1168-1181
    [53] Varadarajan B, Khudanpur S, Tran T D. Stepwise optimal subspace pursuit for improving sparse recovery. IEEE Signal Processing Letters, 2011, 18(1): 27-30
    [54] Bajwa W, Haupt J, Sayeed A, Nowak R. Compressive wireless sensing. In: Proceedings of the 5th International Conference on Information Processing in Sensor Networks. Nashville, TN: IEEE, 2006. 134-142
    [55] Nasser N, Guizani S, Shih S Y, Chen K C. Compressed sensing construction of spectrum map for routing in cognitive radio networks. Wireless Communications Mobile Computing, 2012, 12(18): 1592-1607
    [56] Lu W, Liu Y Z, Wang D S. Efficient feedback scheme based on compressed sensing in MIMO wireless networks. Computers and Electrical Engineering, 2013, 39(6): 1587-1600
    [57] Takhar D, Laska J N, Wakin M B, Duarte M F. A new compressive imaging camera architecture using optical-domain compression. In: Proceedings of Computational Imaging IV at SPIE Electronic Imaging. San Jose, CA: SPIE, 2006. 43-52
    [58] Willett R M, Gehm M E, Brady D J. Multiscale reconstruction for computational spectral imaging. In: Proceedings of the International Society for Optical Engineering. San Jose, CA, USA: SPIE, 2007
    [59] Xu J, Pi Y, Cao Z. Bayesian compressive sensing in synthetic aperture radar imaging. IET Radar, Sonar and Navigation, 2012, 6(1): 2-8
    [60] Zhu X X, Bamler R. Within the resolution cell: super-resolution in tomographic SAR imaging. In: Proceedings of the IEEE International Geoscience and Remote Sensing Symposium. Vancouver, BC: IEEE, 2011. 2401-2404
    [61] Huan Y F, Wang J F, Zhen T, Liu X Z. SAR imaging based on compressed sensing. In: Proceedings of the IEEE International of Geoscience and Remote Sensing Symposium. Vancouver, BC: IEEE, 2011. 1674-1677
    [62] Quan Y H, Zhang L, Guo R, Xing M D, Bao Z. Generating dense and super-resolution ISAR image by combining bandwidth extrapolation and compressive sensing. Science China Information Sciences, 2011, 54(10): 2158-2169
    [63] Zhao G H, Wang Z Y, Wang Q, Shi G M, Shen F F. Robust ISAR imaging based on compressive sensing from noisy measurements. Signal Processing, 2012, 92(1): 120-129
    [64] Yang J G, Thompson J, Huang X T, Jin T, Zhou Z M. Random-frequency SAR imaging based on compressed sensing. IEEE Transactions on Geoscience and Remote Sensing, 2013, 51(2): 983-994
    [65] Hu S, Lustig M, Chen A P, Crane J, Kerr A, Kelley D A C, Hurd R, Kurhanewicz J, Nelson S J, Pauly J M, Vigneron D B. Compressed sensing for resolution enhancement of hyperpolarized 13C flyback 3D-MRSI. Journal of Magnetic Resonance, 2008, 192(2): 258-264
    [66] Chartrand R. Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data. In: Proceedings of the IEEE International Symposium on Biomedical Imaging: from Nano to Macro. Washington D.C., USA: IEEE, 2009. 262-265
    [67] Qu X B, Zhang W R, Guo D, Cai C B, Cai S H, Chen Z. Iterative thresholding compressed sensing MRI based on contourlet transform. Inverse Problems in Science and Engineering, 2010, 18(6): 737-758
    [68] Haldar J P, Hernando D, Liang Z P. Compressed-sensing MRI with random encoding. IEEE Transactions on Medical Imaging, 2011, 30(4): 893-903
    [69] Daehyun K, Trzasko J D, Smelyanskiy M, Haider C R. High-performance 3D compressive sensing MRI reconstruction. In: Proceedings of the International Conference of the Engineering in Medicine and Biology Society. Buenos Aires: IEEE, 2010. 3321-3324
    [70] Majumdar A, Ward R K. Accelerating multi-echo T2 weighted MR imaging: analysis prior group-sparse optimization. Journal of Magnetic Resonance, 2011, 210(1): 90-97
    [71] Jafarpour S, Pezeshki A, Calderbank R. Experiments with compressively sampled images and a new debluring-denoising algorithm. In: Proceedings of the 10th IEEE International Symposium on Multimedia. Berkeley, CA: IEEE, 2008. 66-73
    [72] Ma J W, Le Dimet F X. Deblurring from highly incomplete measurements for remote sensing. IEEE Transactions on Geoscience and Remote Sensing, 2009, 47(3): 792-802
    [73] Ma J W. Improved iterative curvelet thresholding for compressed sensing and measurement. IEEE Transactions on Instrumentation and Measurement, 2011, 60(1): 126-136
    [74] He M Y, Liu W H, Bai L. Remote sensing image restoration based on compressive sensing and two-step iteration shrinkage algorithm. In: Proceedings of SPIEThe International Society for Optical Engineering. San Diego, California: SPIE, 2010
    [75] Divekar A, Ersoy O. Image fusion by compressive sensing. In: Proceedings of the 17th International Conference on Geoinformatics. Fairfax, VA: IEEE, 2009. 1-6
    [76] Tao W, Canagarajah N, Achim A. Compressive image fusion. In: Proceedings of the 15th IEEE International Conference on Image Processing. San Diego, CA: IEEE, 2008. 1308-1311
    [77] Wen J T, Chen Z Y, Han Y X, Villasenor J D. A compressive sensing image compression algorithm using quantized DCT and noiselet information. In: Proceedings of the 2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP). Dallas, TX: IEEE, 2010. 1294-1297
    [78] Du Zhuo-Ming, Geng Guo-Hua, He Yi-Yue. A 2-D geo-metric signal compression method based on compressed sensing. Acta Automatica Sinica, 2012, 38(11): 1841-1846(杜卓明, 耿国华, 贺毅岳. 一种基于压缩感知的二维几何信号压缩方法. 自动化学报, 2012, 38(11): 1841-1846)
    [79] Huo C F, Zhang R, Yin D. Compression technique for compressed sensing hyperspectral images. International Journal of Remote Sensing, 2011, 33(5): 1586-1604
    [80] Yang J C, Wright J, Huang T, Ma Y. Image super-resolution as sparse representation of raw image patches. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Washington D.C., USA: IEEE, 2008. 1-8
    [81] Sen P, Darabi S. Compressive image super-resolution. In: Proceedings of the 43rd Asilomar Conference on Signals, Systems and Computers. Pacific Grove, CA: IEEE, 2009. 1235-1242
    [82] Edeler T, Ohliger K, Hussmann S, Mertins A. Multi image super resolution using compressed sensing. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing. Washington D.C., USA: IEEE, 2011. 2868-2871
    [83] Gurbuz A C, McClellan J H, Romberg J, Scott W R. Compressive sensing of parameterized shapes in images. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing. Las Vegas, NV: IEEE, 2008. 1949-1952
    [84] Hou Q, Pan H P, Li J, Wu T. Image feature extraction based on compressive sensing with application of image denoising. In: Proceedings of the International Conference on Electrical and Control Engineering. Wuhan, China: IEEE, 2010. 1154-1157
    [85] Wright J, Yang A Y, Ganesh A, Sastry S S. Robust face recognition via sparse representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31(2): 210-227
    [86] Liang S F, Wang Y, Liu Y H. Face recognition algorithm based on compressive sensing and SRC. In: Proceedings of the 2nd International Conference on Instrumentation, Measurement, Computer, Communication and Control. Harbin, China: IEEE, 2012. 1460-1463
    [87] Nagesh P, Li Baoxin. A compressive sensing approach for expression-invariant face recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Washington D.C., USA: IEEE, 2009. 1518-1525
    [88] He Chu, Liu Ming, Feng Qian, Deng Xin-Ping. PolInSAR image classification based on compressed sensing and multi-scale pyramid. Acta Automatica Sinica, 2011, 37(7): 820-827(何楚, 刘明, 冯倩, 邓新萍. 基于多尺度压缩感知金字塔的极化干涉SAR图像分类. 自动化学报, 2011, 37(7): 820-827)
    [89] Cheng C, Ming Z, Ping Z J. Weed seeds classification based on compressive sensing theory. Science China Information Sciences, 2010, 40(S1): 160-172
    [90] Ren Y M, Zhang Y N, Li Y, Huang J Y, Hui J. A space target recognition method based on compressive sensing. In: Proceedings of the 6th International Conference on Image and Graphics. Hefei, China: IEEE, 2011. 582-586
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  • 收稿日期:  2012-02-28
  • 修回日期:  2013-12-18
  • 刊出日期:  2014-08-20

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