字典学习模型、算法及其应用研究进展

练秋生; 石保顺; 陈书贞

doi:10.16383/j.aas.2015.c140252

字典学习模型、算法及其应用研究进展

doi: 10.16383/j.aas.2015.c140252

1.
燕山大学信息科学与工程学院秦皇岛 066004

基金项目:

国家自然科学基金(61471313),河北省自然科学基金(F2014203076)资助

详细信息

作者简介:
石保顺燕山大学信息科学与工程学院博士研究生. 主要研究方向为图像处理,盲压缩感知, 字典学习.E-mail: shibaoshun1989@163.com

陈书贞燕山大学信息科学与工程学院副教授. 主要研究方向为图像处理, 压缩感知及生物识别.E-mail: chen sz818@163.com

通讯作者:
练秋生燕山大学信息科学与工程学院教授. 主要研究方向为图像处理, 稀疏表示, 压缩感知及多尺度几何分析. 本文通信作者. E-mail: lianqs@ysu.edu.cn

计量
- 文章访问数: 6271
- HTML全文浏览量: 148
- PDF下载量: 5360
- 被引次数: 0
出版历程
- 收稿日期: 2014-04-14
- 修回日期: 2014-10-12
- 刊出日期: 2015-02-20

Research Advances on Dictionary Learning Models, Algorithms and Applications

1.
School of Information Science and Engineering, Yanshan University, Qinhuangdao 066004

Funds:

Supported by National Natural Science Foundation of China (61471313), and Natural Science Foundation of Hebei Province (F2014203076)

摘要

摘要: 稀疏表示模型常利用训练样本学习过完备字典, 旨在获得信号的冗余稀疏表示. 设计简单、高效、通用性强的字典学习算法是目前的主要研究方向之一, 也是信息领域的研究热点. 基于综合稀疏模型的字典学习方法已经广泛应用于图像分类、图像去噪、图像超分辨率和压缩成像等领域. 近些年来, 解析稀疏模型、盲字典模型和信息复杂度模型等新模型的出现丰富了字典学习理论, 使得更广泛类型的信号能够被简单性描述. 本文详细介绍了综合字典、解析字典、盲字典和基于信息复杂度字典学习的基本模型及其算法, 阐述了字典学习的典型应用, 指出了字典学习的进一步研究方向.
- 字典学习 /
- 稀疏表示 /
- 综合模型 /
- 解析模型
Abstract: The sparse model often utilizes training samples to learn an over-complete dictionary, in order to obtain the redundant and sparse representation of signals. Designing simple, effective and flexible dictionary learning algorithms is one of the main and hot research topics in the information field. The dictionary learning methods based on synthesis sparse model have been applied into image classification, image denoising, image super-resolution and compressive imaging. In recent years, analysis sparse model, blind dictionary model and information complexity model have been proposed, which enrich the dictionary learning theory in order and lead to a simple description for a wide range of signals. In this paper, the fundamental models and dictionary learning algorithms are introduced in detail in terms of synthesis dictionary, analysis dictionary, blind dictionary and dictionary learning based on information complexity. Typical applications of dictionary learning methods are further illustrated. Finally, the directions for further research of the dictionary learning are pointed out.
- Dictionary learning /
- sparse representation /
- synthesis model /
- analysis model

HTML全文

参考文献(132)

[1]	Hubel D H, Wiesel T N. Receptive fields of single neurons in the cat's striate cortex. Journal of Physiology, 1959, 148(3): 574-591
[2]	[2] Willshaw D J, Buneman O P, Longuet-Higgins H C. Non-holographic associative memory. Nature, 1969, 222(5197): 960-962
[3]	[3] Barlow H B. Single units and sensation: A neuron doctrine for perceptual psychology? Perception, 1972, 1(4): 371-394
[4]	[4] Oja E. Simplified neuron model as a principal component analyzer. Journal of Mathematical Biology, 1982, 15(3): 267-273
[5]	[5] Pham T T, Defigueiredo R J P. Maximum likelihood estimation of a class of non-Gaussian densities with application to L_p deconvolution. IEEE Transaction on Acoustics, Speech, and Signal Process, 1989, 37(1): 73-82
[6]	[6] Jutten C, Herault J. Blind separation of sources, Part I: an adaptive algorithm based on neuromimetic architecture. Signal Processing, 1991, 24(1): 1-10
[7]	[7] Mallat S, Zhang Z. Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing, 1993, 41(12): 3397-3415
[8]	[8] Chen S S, Donoho D L. Saunders M A. Atomic Decomposition by Basis Pursuit. Technical Report, Stanford University, Britain, 1995.
[9]	[9] Olshausen B A, Field D J. Emergency of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 1996, 381(6583): 607-609
[10]	Olshausen B A, Field D J. Natural image statistics and efficient coding. Network Computation in Neural Systems, 1996, 7(2): 333-339
[11]	Olshausen B A, Field D J. Sparse coding with an overcomplete basis set: a strategy employed by V1? Vision Research, 1997, 37(23): 3311-3325
[12]	Donoho D L. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306
[13]	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
[14]	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, 吴娇, 杨淑媛, 焦李成. 结构化压缩感知进展. 自动化学报, 2013, 39(12): 1980-1995)
[15]	Mallat S. Geometrical grouplets. Applied and Computational Harmonic Analysis, 2009, 26(2): 161-180
[16]	Yaghoobi M, Daudet L, Davies M E. Parametric dictionary design for sparse coding. IEEE Transactions on Signal Processing, 2009, 57(12): 4800-4810
[17]	Elad M, Aharon M. Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Signal Processing, 2006, 15(12): 3736-3745
[18]	Liu J J, Ma X H. An improved image inpainting algorithm based on multi-scale dictionary learning in wavelet domain. In: Proceedings of the 2013 International Conference on Signal Processing, Communication and Computing. Kunming, China: IEEE, 2013. 1-5
[19]	Liu X M, Zhai D M, Zhao D B, Gao W. Image super-resolution via hierarchical and collaborative sparse representation. In: Proceedings of the 2013 Data Compression Conference. Snowbird, USA: IEEE, 2013. 93-102
[20]	Aharon M, Elad M, Bruckstein A M. The K-SVD: an algorithm for designing of overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 2006, 54(11): 4311-4322
[21]	Yaghoobi M, Blumensath T, Davies M E. Dictionary learning for sparse approximations with the majorization method. IEEE Transactions on Signal Processing, 2009, 57(6): 2178-2191
[22]	Mairal J, Bach F, Ponce J, Sapiro G. Online learning for matrix factorization and sparse coding. Journal of Machine Learning Research, 2010, 11(1): 19-60
[23]	Zelnik-Manor L, Rosenblum K, Eldar Y C. Dictionary optimization for block-sparse representations. IEEE Transactions on Signal Processing, 2012, 60(5): 2386-2395
[24]	Elad M, Milanfar P, Rubinstein R. Analysis versus synthesis in signal priors. Inverse Problems, 2007, 23(3): 947-968
[25]	Rubinstein R, Bruckstein A M, Elad M. Dictionaries for sparse representation modeling. Proceedings of the IEEE, 2010, 98(6): 1045-1057
[26]	Nam S, Davies M E, Elad M, Gribonval R. The cosparse analysis model and algorithms. Applied and Computational Harmonic Analysis, 2013, 34(1): 30-56
[27]	Gleichman S, Eldar Y C. Blind compressed sensing. IEEE Transactions on Information Theory, 2011, 57(10): 6958-6975
[28]	Jalali S, Maleki A. Minimum complexity pursuit. In: Proceedings of the 49th Annual Allerton Conference on Communication, Control, and Computing. Monticello, IL: IEEE, 2011. 1764-1770
[29]	Ramirez I, Sapiro G. An MDL framework for sparse coding and dictionary learning. IEEE Transactions on Signal Processing, 2012, 60(6): 2913-2927
[30]	Donoho D L, Tsaig Y, Drori I, Starck J L. Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Transactions on Information Theory, 2012, 58(2): 1094-1121
[31]	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): 1070-1081 (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): 1070-1081)
[32]	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
[33]	Dai W, Milenkovic O. Subspace pursuit for compressive sensing signal. IEEE Transaction on Information Theory, 2009, 55(5): 2230-2249
[34]	Ambat S K, Chatterjee S, Hari K V S. Fusion of algorithms for compressed sensing. IEEE Transactions on Signal Processing, 2013, 61(14): 3699-3704
[35]	Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 1998, 20(1): 33-61
[36]	Tibshirani R. Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society Series B, 1996, 58(1): 267-288
[37]	Lewicki M S, Olshausen B A. Probabilistic framework for the adaptation and comparison of image codes. Journal of the Optical Society of America a Optics Image Science and Vision, 1999, 16(7): 1587-1601
[38]	Kreutz-Delgado K, Murray J F, Rao B D, Engan K, Lee T W, Sejnowski T J. Dictionary learning algorithms for sparse representation. Neural Computation, 2003, 15(2): 349-396
[39]	Mailh B, Plumbley M D. Dictionary learning with large step gradient descent for sparse representations. In: Proceedings of the 10th International Conference on Latent Variable Analysis and Signal Separation. Berlin, Heidelberg: Springer, 2012. 231-238
[40]	Lee H, Battle A, Raina R, Ng A Y. Efficient sparse coding algorithms. In: Proceedings of the 20th Annual Conference on Neural Information Processing Systems. Columbia, Canada: IEEE, 2006. 801-808
[41]	Engan K, Aase S O, Husoy J H. Method of optimal directions for frame design. In: Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Phoenix AZ: IEEE, 1999. 2443-2446
[42]	Smith L N, Elad M. Improving dictionary learning: multiple dictionary updates and coefficient reuse. IEEE Signal Processing Letters, 2013, 20(1): 79-82
[43]	Rubinstein R, Zibulevsky M, Elad M. Efficient Implementation of the K-SVD Algorithm Using Batch Orthogonal Matching Pursuit, Technical Report, Technion University, Israel, 2008.
[44]	Sadeghi M, Babaie-Zadeh M, Jutten C. Learning overcomplete dictionaries based on parallel atom-updating. In: Proceedings of the 2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP). Southampton, UK: IEEE, 2013. 1-5
[45]	Dai W, Xu T, Wang W. Simultaneous codeword optimization (SimCO) for dictionary update and learning. IEEE Transactions on Signal Processing, 2012, 60(12): 6340-6353
[46]	Rusu C, Dumitrescu B. Stagewise K-SVD to design efficient dictionaries for sparse representations. IEEE Signal Processing Letters, 2012, 19(10): 631-634
[47]	Lu C W, Shi J P, Jia J Y. Scale adaptive dictionary learning. IEEE Transactions on Image Processing, 2014, 23(2): 837-847
[48]	Sahoo S K, Makur A. Dictionary training for sparse representation as generalization of K-means clustering. IEEE Signal Processing Letters, 2013, 20(6): 587-590
[49]	Sadeghi M, Babaie-Zadeh M, Jutten C. Dictionary learning for sparse representation: a novel approach. IEEE Signal Processing Letters, 2013, 20(12): 1195-1198
[50]	Rakotomamonjy A. Applying alternating direction method of multipliers for constrained dictionary learning. Neurocomputing, 2013, 106: 126-136
[51]	Rakotomamonjy A. Direct optimization of the dictionary learning problem. IEEE Transactions on Signal Processing, 2013, 61(22): 5495-5506
[52]	Sigg C D, Dikk T, Buhmann J M. Learning dictionaries with bounded self-coherence. IEEE Signal Processing Letters, 2012, 19(12): 861-864
[53]	Mailhe B, Barchiesi D, Plumbley M D. INK-SVD: learning incoherent dictionaries for sparse representations. In: Proceedings of the 2012 International Conference on Acoustics, Speech and Signal Processing. Kyoto, Japan: IEEE, 2012. 3573-3576
[54]	Barchiesi D, Plumbley M D. Learning incoherent dictionaries for sparse approximation using iterative projections and rotations. IEEE Transactions on Signal Processing, 2013, 61(8): 2055-2065
[55]	Skretting K, Engan K. Recursive least squares dictionary learning algorithm. IEEE Transactions on Signal Processing, 2010, 58(4): 2121-2130
[56]	Labusch K, Barth E, Martinetz T. Robust and fast learning of sparse codes with stochastic gradient descent. IEEE Transactions on Selected Topics in Signal Processing, 2011, 5(5): 1048-1060
[57]	Sendur L, Selesnick I W. Bivariate shrinkage functions for wavelet based denoising exploiting interscale dependency. IEEE Transactions on Signal Processing, 2002, 50(11): 2744-2756
[58]	Lesage S, Gribonval R, Bimbot F, Benaroya L. Learning unions of orthonormal bases with thresholded singular value decomposition. In: Proceedings of the 2005 International Conference on Acoustics, Speech and Signal Processing. Philadelphia, PA: IEEE, 2005. 293- 296
[59]	Vidal R, Ma Y, Sastry S. Generalized principal component analysis (GPCA). IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(12): 1945-1959
[60]	Bengio S, Pereira F, Singer Y, Strelow D. Group sparse coding. In: Proceedings of the 23rd Annual Conference on Neural Information Processing Systems. Vancouver, British Columbia, Canada: IEEE, 2009. 82-89
[61]	Szabo Z, Poczos B, Lorincz A. Online group-structured dictionary learning. In: Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition. Providence, RI: IEEE, 2011. 2865-2872
[62]	Jenatton R, Mairal J, Obozinski G, Bach F. Proximal methods for hierarchical sparse coding. Journal of Machine Learning Research, 2011, 12(7): 2297-2334
[63]	Mairal J, Sapiro G, Elad M. Learning multiscale sparse representations for image and video restoration. Multiscale Modeling and Simulation, 2008, 7(1): 214-241
[64]	Ophir B, Lustig M, Elad M. Multi-scale dictionary learning using wavelets. IEEE Journal of Selected Topics in Signal Processing. 2011, 5(5): 1014-1024
[65]	Thiagarajan J J, Ramamurthy K N, Spanias A. Multilevel dictionary learning for sparse representation of images. In: Proceedings of the 2011 IEEE Digital Signal Processing Workshop and Signal Processing Education Workshop. Sedona, AZ: IEEE, 2011. 271-276
[66]	Rubinstein R, Zibulevsky M, Elad M. Double sparsity: learning sparse dictionaries for sparse signal approximation. IEEE Transactions on Signal Processing, 2010, 58(3): 1553-1564
[67]	Yaghoobi M, Davies M E. Compressible dictionary learning for fast sparse approximations. In: Proceedings of the 15th IEEE/SP Workshop on Statistical Signal Processing. Cardiff: IEEE, 2009. 662-665
[68]	Hawe S, Seibert M, Kleinsteuber M. Separable dictionary learning. In: Proceedings of the 2013 IEEE Conference on Computer Vision and Pattern Recognition. Washington D.C., USA: IEEE, 2013. 438-445
[69]	Jost P, Vandergheynst P, Lesage S, Gribonval R. MoTIF: an efficient algorithm for learning translation invariant dictionaries. In: Proceedings of the 2006 IEEE International Conference on Acoustics, Speech and Signal Processing. Toulouse, France: IEEE, 2006. 5
[70]	Aharon M, Elad M. Sparse and redundant modeling of image content using an image-signature-dictionary. SIAM Journal on Imaging Sciences, 2008, 1(3): 228-247
[71]	Rusu C, Dumitrescu B, Tsaftaris S A. Explicit shift-invariant dictionary learning. IEEE Signal Processing Letters, 2014, 21(1): 6-9
[72]	Pope G, Aubel C, Studer C. Learning phase-invariant dictionaries. In: Proceedings of the 2013 International Conference on Acoustics, Speech and Signal Processing. Vancouver, Canada: IEEE, 2013. 5979-5983
[73]	Zhou M, Yang H, Paisley J, Ren L. Nonparametric Bayesian dictionary learning for analysis of noisy and incomplete images. IEEE Transactions on Image Processing, 2012, 21(1): 130-144
[74]	Ravishankar S, Bresler Y. Learning sparsifying transform. IEEE Transactions on Signal Processing, 2013, 61(5): 1072-1086
[75]	Rubinstein R, Peleg T, Elad M. Analysis K-SVD: a dictionary-learning algorithm for the analysis sparse model. IEEE Transactions on Signal Processing, 2013, 61(3): 661-677
[76]	Chen Y J, Ranftl R, Pock T. Insights into analysis operator learning: from patch-based sparse models to higher order MRFs. IEEE Transactions on Image Processing, 2014, 23(3): 1060-1072
[77]	Zhang Y, Wang H L, Yu T L. Subset pursuit for analysis dictionary learning. In: Proceedings of the 21th European Signal Processing Conference. Marrakech, Morocco, 2013. 1-5
[78]	Zhang Y, Wang H L, Wang W W, Sanei S. K-plane clustering algorithm for analysis dictionary learning. In: Proceedings of the 2013 IEEE International Workshop on Machine Learning for Signal Processing. Southampton, Britain: IEEE, 2013. 1-4
[79]	Dong J, Wang W W, Dai W. Analysis SimCO: a new algorithm for analysis dictionary learning. In: Proceedings of the 2014 IEEE International Conference on Acoustics, Speech and Signal Processing. Florence, Italy: IEEE, 2014. 7193-7197
[80]	Yaghoobi M, Nam S, Gribonval R, Davies M E. Constrained overcomplete analysis operator learning for cospaese signal modelling. IEEE Transactions on Signal Processing, 2013, 61(9): 2141-2355
[81]	Yaghoobi M, Davies M E. Relaxed analysis operator learning. In: Proceedings of the 2012 NIPS, Workshop on Analysis Operator Learning vs. Dictionary Learning: Fraternal Twins in Sparse Modeling. Lake Tahoe, USA: IEEE, 2012.
[82]	Hawe S, Kleinsteuber M, Diepold K. Analysis operator learning and its application to image reconstruction. IEEE Transactions on Image Processing, 2013, 22(6): 2138-2150
[83]	Ravishankar S, Bresler Y. Sparsifying transform learning for compressed sensing MRI. In: Proceedings of the 10th International Symposium on Biomedical Imaging. San Francisco, CA: IEEE, 2013. 17-20
[84]	Ravishankar S, Bresler Y. Closed-form solutions within sparsifying transform learning. In: Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing. Vancouver, Canada: IEEE, 2013. 5378-5382
[85]	Ravishankar S, Bresler Y. Learning sparsifying transforms for image processing. In: Proceedings of the 2012 19th IEEE International Conference on Image Processing. Orlando, USA: IEEE, 2012. 681-684
[86]	Eksioglu E M, Bayir O. K-SVD meets transform learning: transform K-SVD. IEEE Signal Processing Letters, 2014, 21(3): 347-351
[87]	Qi N,Shi Y H, Sun X Y, Wang J D, Ding W P. Two dimensional analysis sparse model. In: Proceedings of the 20th International Conference on Imaging Processing. Melbourne, Australia: IEEE, 2013. 310-314
[88]	Seibert M, Wrmann J, Gribonval R, Kleinsteuber M. Separable cosparse analysis operator learning. In: Proceedings of the 22nd European Signal Processing Conference (EUSIPCO). Lisbonne, Portuga, 2014.
[89]	Ravishankar S, Bresler Y. Learning doubly sparsifying transforms for images. IEEE Transactions on Image Processing, 2013, 22(12): 4598-4612
[90]	Anaraki P F, Hughes S M. Compressive K-SVD. In: Proceedings of the 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing. Vancouver, Canada: IEEE, 2013. 5469-5473
[91]	Aghagolzadeh M, Radha H. Compressive dictionary learning for image recovery. In: Proceedings of the 19th IEEE International Conference on Image Processing. Orlando, USA: IEEE, 2012. 661-664
[92]	Ravishankar S, Bresler Y. MR image reconstruction from highly undersampled k-space data by dictionary learning. IEEE Transactions on Medical Imaging, 2011, 30(5): 1028-1041
[93]	Zhang J, Zhao C, Zhao D B, Gao W. Image compressive sensing recovery using adaptively learned sparsifying basis via L0 minimization. Signal Processing, 2014, 103: 114-126
[94]	Goldstein T, Osher S. The split Bregman algorithm for L1 regularized problems. SIAM Journal on Imaging Sciences, 2009, 2(2): 323-343
[95]	Chen C, Tramel E W, Fowler J E. Compressed-sensing recovery of images and video using multi-hypothesis predictions. In: Proceedings of the 45th Asilomar Conference on Signals, Systems, and Computers. Pacific Grove, USA: IEEE, 2011. 1193-1198
[96]	Wormann J, Hawe S, Kleinsterber M. Analysis based blind compressive sensing. IEEE Signal Processing Letters, 2013, 20(5): 491-494
[97]	Jalali S, Maleki A, Baraniuk R G. Minimum complexity pursuit for universal compressed sensing. IEEE Transactions on Information Theory, 2014, 60(4): 2253-2268
[98]	Kolmogorov A N. Logical basis for information theory and probability theory. IEEE Transactions on Information Theory, 1968, 14(5): 662-664
[99]	Rissanen J. Modeling by shortest data description. Automatica, 1978, 14(5): 465-471
[100]	Grunwald P D. The Minimum Description Length Principle. Cambridge: UK Press, 2007.
[101]	Roos T, Myllymaki P, Rissanrien J. MDL denoising revisited. IEEE Transactions on Signal Processing, 2009, 57(9): 3347-3360
[102]	Chang S G, Yu B, Vetterli M. Adaptive wavelet thresholding for image denoising and compression. IEEE Transactions on Image Processing, 2000, 9(9): 1532-1546
[103]	Knaus C, Zwicker M. Dual-domain image denoising. In: Proceedings of the 2013 20th IEEE International Conference on Image Processing. Melbourne, Australia: IEEE, 2013. 440-444
[104]	Beckouche S, Starck J L, Fadili J. Astronomical image denoising using dictionary learning. Astronomy Astrophysics, 2013, 556(6): 14, DOI: 10.1051/0004-6361/ 201220752
[105]	Li S T, Fang L Y, Yin H T. An efficient dictionary learning algorithm and its application to 3-D medical image denoising. IEEE Transactions on Biomedical Engineering, 2012, 59(2): 417-427
[106]	Lian Qiu-Sheng, Zhang Jun-Qin, Chen Shu-Zhen. Single image super-resolution algorithm based on two-stage and multi-frequency -band dictionaries. Acta Automatica Sinica, 2013, 39(8): 1310-1320 (练秋生, 张钧芹, 陈书贞. 基于两级字典与分频带字典的图像超分辨率算法. 自动化学报, 2013, 39(3): 1310-1320)
[107]	Yang J C, Wright J, Huang T, Ma Y. Image super-resolution as sparse representation of raw image patches. In: Proceedings of the 2008 IEEE Conference on Computer Vision and Pattern Recognition. Anchorage, USA: IEEE, 2008. 1-8
[108]	Yang J C, Wright J, Huang T S, Ma Y. Image super-resolution via sparse representation. IEEE Transactions on Image Processing, 2010, 19(11): 2861-2873
[109]	Yang J C, Wang W Z, Lin Z, Cohen S, Huang T. Coupled dictionary training for image super-resolution. IEEE Transaction on Image Processing, 2012, 21(8): 3467-3478
[110]	Lu X Q, Yuan Y, Yan P K. Alternatively constrained dictionary learning for image superresolution. IEEE Transactions on Cybernetics, 2014, 44(3): 366-377
[111]	Wang S L, Zhang L, Liang Y, Pan Q. Semi-coupled dictionary learning with applications to image super-resolution and photo-sketch synthesis. In: Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition. Providence, USA: IEEE, 2012. 2216-2223
[112]	Lian Qiu-Sheng, Chen Shu-Zhen. Image reconstruction 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)
[113]	Rajwade A, Kittle D, Tsai T H, Brady D, Carin L. Codes hyperspectral imaging and blind compressive sensing. SIAM Journal on Imaging Sciences, 2013, 6(2): 782-812
[114]	Lingala S G, Jacob M. A blind compressive sensing frame work for accelerated dynamic MRI. In: Proceedings of the 9th IEEE International Symposium on Biomedical Imaging (ISBI). Barcelona, Spain: IEEE, 2012. 1060-1063
[115]	Huang J Z, Zhang S T, Metaxas D. Efficient MR image reconstruction for compressed MR imaging. Medical Image Analysis, 2011, 15(5): 670-679
[116]	Wright J, Yang A, Ganesh A, Sastry S, Ma Y. Roubust face recognition via sparse representation. Pattern Analysis and Machine Intelligence, 2009, 31(2): 210-227
[117]	Yang M, Zhang L, Yang J, Zhang D. Metaface learning for sparse representation based face recognition. In: Proceedings of the 17th IEEE International Conference on Image Processing. Hong Kong, China: IEEE, 2010. 1601-1604
[118]	Ramirez I, Sprechmann P, Sapiro G. Classification and clustering via dictionary learning with structured incoherence and shared features. In: Proceedings of the 2010 IEEE Conference on Computer Vision and Pattern Recognition. San Francisco, USA: IEEE, 2010. 3501-3508
[119]	Mairal J, Bach F, Ponce J. Task-driven dictionary learning. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 34(4): 791-804
[120]	Zhang Q, Li B Q. Discriminative K-SVD for dictionary learning in face recognition. In: Proceedings of the 2010 IEEE Conference on Computer Vision and Pattern Recognition. San Francisco, USA: IEEE, 2010. 2691-2698
[121]	Yang M, Zhan D, Feng X C, Zhang D. Fisher discrimination dictionary learning for sparse representation. In: Proceedings of the 2011 IEEE International Conference on Computer Vision. Barcelona, Spain: IEEE, 2011. 543-550
[122]	Nguyen H V, Patel V M, Nasrabadi N M, Chellapa R. Kernel dictionary learning. In: Proceedings of the 2012 IEEE International Conference on Acoustics, Speech and Signal Processing Kyoto, Japan: IEEE, 2012. 2021-2024
[123]	Duarte-Carvejalino J M, Sapiro G. Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization. IEEE Transactions on Image Processing, 2009, 18(7): 1395-1408
[124]	Chen W, Rodrigues M R D. Dictionary learning with optimized projection design for compressive sensing applications. IEEE Signal Processing Letters, 2013, 20(10): 992-995
[125]	Zhang Hai, Wang Yao, Chang Xiang-Yu, Xu Zong-Ben. L1/2 regularization. Science China: Information Sciences, 2010, 40(3): 412-422 (张海, 王尧, 常象宇, 徐宗本. L1/2 正则化. 中国科学: 信息科学, 2010, 40(3): 412-422)
[126]	Xu Z B, Chang X Y, Xu F M, Zhang H. L1/2 regularization: a thresholding representation theory and a fast solver. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(7): 1013-1027
[127]	Zuo W M, Meng D Y, Zhang L, Feng X C, Zhang D. A generalized iterated shrinkage algorithm for non-convex sparse coding. In: Proceedings of the 2013 IEEE International Conference on Computer Vision. Sydney, Australia: IEEE, 2013. 217-244
[128]	Candes E J, Plan Y. Matrix completion with noise. Proceedings of the IEEE, 2010, 98(6): 925-936
[129]	Cands E J, Recht B. Simple bounds for recovering low-complexity models. Mathematical Programming, 2013, 141(1-2): 577-589
[130]	Peng Yi-Gang, Suo Jin-Li, Dai Qiong-Hai, Xu Wen-Li. From compressed sensing to low-rank matrix recovery: theory and applications. Acta Automatica Sinica, 2013, 39(7): 981-994 (彭义刚, 索津莉, 戴琼海, 徐文立. 从压缩传感到低秩矩阵恢复: 理论与应用. 自动化学报, 2013, 39(7): 981-994)
[131]	Elad M. Sparse and redundant representation modeling-what next? IEEE Signal Processing Letters, 2012, 19(12): 922-928
[132]	Bao C L, Ji H, Quan Y H, Shen Z W. L0 norm based dictionary learning by proximal methods with global convergence. In: Proceedings of the 2014 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Portland, USA: IEEE, 2013. 3858-3865