图像压缩感知理论研究综述
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摘要
随着人们对图像数据需求的增大,传统的Nyquist采样理论会产生大量的采样数据,为图像数据的传输和存储带来莫大的困难,压缩感知理论为此难题的解决找到了有效途径,对于可压缩或可稀疏的信号,它能以远远低于Nyquist的采样频率,通过观测矩阵进行非自适应采样,利用重构算法准确重构原始信号。着重介绍了图像压缩感知的理论框架和一些前沿研究算法,并对其进行比较,总结了压缩感知在图像领域的研究近况与应用前景。
With the great demand for image information,if the traditional Nyquist sampling theory is used,a huge amount of sampled data is produced,it is a great burden to following data processing. The theory of compressed sensing can be used to effectively solve this problem. If it is the compressed or sparse signal,the sampling frequency is much lower than the Nyquist sampling frequency,the measurement matrix can be used for the unadaptable sampling and the reconstruction algorithm can be used to accurately reconstruct the original signal. This paper focuses on introducing the theoretical framework of image compression sensing and some of the leading-edge algorithms,makes a comparison,then,summarizes the current research status and application prospects of compressed sensing in the image domain.
With the great demand for image information,if the traditional Nyquist sampling theory is used,a huge amount of sampled data is produced,it is a great burden to following data processing. The theory of compressed sensing can be used to effectively solve this problem. If it is the compressed or sparse signal,the sampling frequency is much lower than the Nyquist sampling frequency,the measurement matrix can be used for the unadaptable sampling and the reconstruction algorithm can be used to accurately reconstruct the original signal. This paper focuses on introducing the theoretical framework of image compression sensing and some of the leading-edge algorithms,makes a comparison,then,summarizes the current research status and application prospects of compressed sensing in the image domain.
引文
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[2]E Candès,J Romberg,Terence Tao. Robust uncertainty principles:Exact signal reconstruct-tion from highly incomplete frequency informa-tion[J]. IEEE Trans. on Information Theory,2006,52(2):489-509.
[3]E Candès and T Tao. Near optimal signal recovery from random projections:Universal encoding strategies[J]. IEEE Trans. Info.Theory,2006,52(12):5406-5425.
[4]D Donoho. Compressed sensing[J]. IEEE Trans. on Information Theory,2006,52(4):1289-1306.
[5]焦李成,杨淑媛,刘芳,等.压缩感知回顾与展望[J].电子学报,2011,39(7):1651-1662.
[6]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[J].自动化学报,2014(8):1563-1575.
[7]Gan L. Block compressed sensing of natural images[C]//Proceedings of the 15th IEEE Inter-national Conference on Digital Signal Process-ing.Cardiff,UK:IEEE,2007:403-406.
[8] Candes E. Ridgelet:Theory and Application[D]. California:Stanford University,1998.
[9]Candes E,Donoho D L. Curvelets[R]. California:Stanford University,1999.
[10]Figueras I,Ventura R M,Vandergheynst P,Frossard P. Lowrate and flexible image coding with redundant representations[J]. IEEE Transac-tions on Image Processing,2006,15(3):726-739.
[11]Rutledge G,Mclean G. Dictionary Projection Pursuit:A Wavelet Packet Technique for Wave-form Feature Extraction[J].Acta Automatica sinica,2001,18(4):104-108.
[12]Xiao L,Shao W Z,Sun Y B,et al. Sparse Representations of Images by a Multi-component Gabor Perception Dictionary[J].Acta Automa-tica Sinica,2008,34(11):1379-1387.
[13]Aharon M,Elad M,Bruckstein A. The K-SVD:an algorithm for designing of over complete dictionaries for sparse representation[J]. IEEE Transactions on Signal Processing,2006,54(11):4311-4322.
[14]Engan K,Aase S,Husoy J. Method of optimal directions for frame design[J]. IEEE Transaction on International Conference on Acoustics,Spee-ch,and Signal Processing,1999(8):2443-2446.
[15]Engan K,Skretting K,Husy J H. Family of iterative LS-based dictionary learning algorithms,ILS-DLA,for sparse signal representation[J]. Digital Signal Processing,2007,17(1):32-49.
[16]Olshausen B,Field D. Emergency of simple-cell receptive fleld properties by learning a sparse code for natural images[J]. Nature,1996,381:607-609.
[17]王红亮,王帅,刘文怡.压缩感知实现方法及其应用综述[J].探测与控制学报,2014(4):53-61.
[18]焦李成,谭山.图像的多尺度几何分析:回顾和展望[J].电子学报,2003,31(S1):1975-1981.
[19]Sahoo S K,Makur A. Replacing K-SVD with SGK:Dictionary Training for Sparse Representa-tion of Images[J]. IEEE International Conference on Digital Signal Processing(DSP),2006,54(11):4311-4316.
[20]Sahoo S K,Makur A. Dictionary training for sparse representation as generalization of K-means clustering[J]. IEEE Signal Processing Letters,2013,20(6):587-590.
[21]练秋生,石保顺,陈书贞.字典学习模型、算法及其应用研究进展[J].自动化学报,2015,41(2):240-260.
[22]Rubinstein R,Zibulevsky M,Elad M. Double Sparsity:Learning Sparse Dictionaries for Sparse Signal Approximation[J]. IEEE Transactions on Signal Processing,2010,58(3):1553-1564.
[23]Gleichman S,Eldar Y C. Blind compressed sensing[J]. IEEE Transactions on Information Theory,2011,57(10):6958-6975.
[24]Y Tsaig,D Donoho. Extensions of compressed sensing[J]. Signal Processing,2006,86(3):549-571.
[25]Tsaig,Yaakov,Donoho,et al. Extensions of compressed sensing[J]. Signal Processing,2006,86(3):549-571.
[26]Fang H,Zhang Q,Sui A W. A Method of Image Reconstruction Based on Sub-Gaussian Random Projection[J]. Journal of Computer Research&Development,2008,45(8):210-214.
[27]Gilbert A C,Guha S,Indyk P,et al. Near-optimal sparse fourier representations via sampling.[C]//on ACM Symposium on Theory of Computing,May,2002:19-21.
[28] Do T T,Tran T D,Gan L. Fast compressive sampling with structurally random matrices[C]//IEEE International Conference on Acoustics, Speech and Signal Processing, IEEE,2008:3369-3372.
[29]Candes E J,Tao T. Near-Optimal Signal Recovery From Random Projections:Universal Encoding Strategies[J]. IEEE Transactions on Information Theory,2006,52(12):5406-5425.
[30]Bajwa W U,Haupt J D,Raz G M,et al. Toeplitz-Structured Compressed Sensing Matri-ces[C]//Statistical Signal Processing,2007. Ssp'07. Ieee/sp,Workshop on. IEEE,2007:294-298.
[31] Applebaum L,Howard S D,Searle S,et al. Chirp sensing codes:Deterministic compressed sensing measurements for fast recovery[J]. Applied&Computational Harmonic Analysis,2009,26(2):283-290.
[32]武昕,王岩飞,刘畅.基于压缩感知理论的随机噪声雷达目标检测算法研究[J].电子与信息学报,2012,34(7):1609-1615.
[33]孟庆微,黄建国,何成兵,等.采用时域测量矩阵的压缩感知稀疏信道估计方法[J].西安交通大学学报,2012,46(8):94-99.
[34]徐倩,季云云.基于最优观测的语音信号压缩感知[J].南京邮电大学学报(自然科学版),2011,31(6):49-54.
[35]曹玉强,柏森,曹明武.图像自适应分块的压缩感知采样算法[J].中国图象图形学报,2016,21(4):416-424.
[36]王蓉芳,焦李成,刘芳,等.利用纹理信息的图像分块自适应压缩感知[J].电子学报,2013,41(8):1506-1514.
[37]翟雪含,朱卫平,康彬.结合KSVD和分类稀疏表示的图像压缩感知[J].计算机工程与应用,2015(6):193-198.
[38]李蕴华.一种改进的图像分块压缩感知模型[J].计算机工程与应用,2011,25:186-189.
[39]Yu Y,Wang B,Zhang L. Saliency-based compressive sampling for image signals[J]. IEEE Signal Processing Letters,2010,17(11):973-976.
[40]王瑞,余宗鑫,杜林峰,等.结合图像信号显著性的自适应分块压缩采样[J].中国图象图形学报,2013,18(10):1255-1260.
[41]王蓉芳,陈佳伟,焦李成,等.基于视觉显著性的分块自适应压缩感知算法[J].华中科技大学学报:自然科学版,2015(1):127-132.
[42]李然,李艳灵,崔子冠,等.视觉显著性导向的图像压缩感知测量与重建[J].华中科技大学学报:自然科学版,2016(5):13-18.
[43]李珅,马彩文,李艳,等.压缩感知重构算法综述[J].红外与激光工程. 2013(S1):225-232.
[44]邵文泽,韦志辉.压缩感知基本理论:回顾与展望[J].中国图象图形学报,2012,17(1):1-12.
[45]Tropp J A,Gilbert A C. Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit[J]. IEEE Transactions on Information Theory,2007,53(12):4655-4666.
[46]Donoho D L,Tsaig Y,Drori I,et al. Sparse Solution of Underdetermined Systems of Linear Equations by Stage wise Orthogonal Matching Pursuit[J]. IEEE Transactions on Information Theory,2012,58(2):1094-1121.
[47]Blumensath T,Davies M E. Iterative hard thresholding for compressed sensing[J]. Applied&Computational Harmonic Analysis,2008,27(3):265-274.
[48]李志林,陈后金,姚畅.基于谱投影梯度追踪的压缩感知重建算法[J].自动化学报,2012,38(7):1218-1223.
[49]Mészáros C. Regularization techniques in interior point methods[J]. Journal of Computational&Applied Mathematics,2012,236(15):3704-3709.
[50]Figueiredo M A T,Nowak R D,Wright S J. Gradient projection for sparse reconstruction:Application to compressed sensing and other inverse problems[C]//IEEE Journal of Selected Topics in Signal Processing,2007:586-597.
[51]Efron B,Hastie T,Johnstone I,et al.“Least angle regression[J]. Annals of Statistics,2004,1(4):251-259.
[52]Candès E J,Romberg J K,Tao T. Stable signal recovery from incomplete and inaccurate mea-surements[J]. Communications on Pure&Appli-ed Mathematics,2006,59(8):1207-1223.
[53] Zayyani H,Babaiezadeh M,Jutten C. Bayesian Pursuit algorithm for sparse representation[C]//IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE Computer Society,2009:1549-1552.
[54]Wipf D P,Rao B D. Sparse Bayesian learning for basis selection[J]. Signal Processing IEEE Tran-sactions on,2004,52(8):2153-2164.
[55]Wipf D P,Rao B D. An Empirical Bayesian Strategy for Solving the Simultaneous Sparse Approximation Problem[J]. IEEE Transactions on Signal Processing,2007,55(7):3704-3716.
[56] Donoho D L,Maleki A,Montanari A. Message-passing algorithms for compressed sensing[J]. Proceedings of the National Academy of Sciences of the United States of America,2009,106(45):189-193.
[57] Gorodnitsky I F,Rao B D. Sparse signal reconstruction from limited data using FOCUSS:a re-weighted minimum norm algorithm[J]. IEEE Transactions on Signal Processing,2002,45(3):600-616.
[58]Duarte M F,Davenport M A,Takhar D,et al. Single-Pixel Imaging via Compressive Sampling[C]//IEEE Signal Processing Mag,2008:83-91.
[59]Lustig M,Donoho D,Pauly J M. Sparse MRI:The application of compressed sensing for rapid MR imaging[J]. Magnetic Resonance in Medic-ine,2007,58(6):1182.
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