Advances and Perspective on Compressed Sensing and Application on Image Processing
-
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.Abstract: Compressed sensing (CS) can perceive the original structure of signals through a few measured values, and reconstruct the signal by solving an optimal problem accurately. The theory of CS not only reduces the cost of the storage and transmission during the acquisition of images and videos, but also provides new opportunities for the follow-up image processing and recognition, promoting the combination of theory and engineering application. This paper presents the principles of CS, and surveys the latest theory achievements and development of sparse representation, design of measurement matrix and reconstruction algorithm. Then this paper analyzes and discusses the research and development of CS theory in its application of image processing field. In the end, the paper points out the existing problems and the future application.
-
[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
点击查看大图
计量
- 文章访问数: 3304
- HTML全文浏览量: 136
- PDF下载量: 2121
- 被引次数: 0