From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
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[1] H. Whitney. On the Abstract Properties of Linear Dependence , 1935 .
[2] L. Karlovitz,et al. Construction of nearest points in the Lp, p even, and L∞ norms. I , 1970 .
[3] Cuthbert Daniel,et al. Fitting Equations to Data: Computer Analysis of Multifactor Data , 1980 .
[4] K. Bellmann. Daniel, C., F. S. WOOD, J. W. GORMAN: Fitting Equations to Data. Computer Analysis of Multifactor Data for Scientists and Engineers. John Wiley & Sons, New York-London-Sydney-Toronto 1974. XIV, 342 S., 132 Abb., 33 Tab., £6.50 , 1975 .
[5] J. Kruskal. Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics , 1977 .
[6] Jim Lawrence,et al. Oriented matroids , 1978, J. Comb. Theory B.
[7] Gene H. Golub,et al. Matrix computations , 1983 .
[8] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.
[9] F. Santosa,et al. Linear inversion of ban limit reflection seismograms , 1986 .
[10] D. Donoho,et al. Uncertainty principles and signal recovery , 1989 .
[11] Sheng Chen,et al. Orthogonal least squares methods and their application to non-linear system identification , 1989 .
[12] G. Pisier. The volume of convex bodies and Banach space geometry , 1989 .
[13] S. Szarek. Spaces with large distance to l∞n and random matrices , 1990 .
[14] Stanislaw J. Szarek,et al. Condition numbers of random matrices , 1991, J. Complex..
[15] Allen Gersho,et al. Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.
[16] L. Rudin,et al. Nonlinear total variation based noise removal algorithms , 1992 .
[17] Edward H. Adelson,et al. Shiftable multiscale transforms , 1992, IEEE Trans. Inf. Theory.
[18] T.,et al. Shiftable Multi-scale TransformsEero , 1992 .
[19] Ronald A. DeVore,et al. Image compression through wavelet transform coding , 1992, IEEE Trans. Inf. Theory.
[20] B. Sturmfels. Oriented Matroids , 1993 .
[21] Y. C. Pati,et al. Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.
[22] Stéphane Mallat,et al. Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..
[23] I. Johnstone,et al. Ideal spatial adaptation by wavelet shrinkage , 1994 .
[24] Zhifeng Zhang,et al. Adaptive time-frequency decompositions , 1994 .
[25] Ronald R. Coifman,et al. Adapted waveform analysis as a tool for modeling, feature extraction, and denoising , 1994 .
[26] I. Johnstone,et al. Ideal denoising in an orthonormal basis chosen from a library of bases , 1994 .
[27] Ronald R. Coifman,et al. Signal processing and compression with wavelet packets , 1994 .
[28] I. Johnstone,et al. Wavelet Shrinkage: Asymptopia? , 1995 .
[29] David L. Donoho,et al. De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.
[30] D. Donoho,et al. Translation-Invariant DeNoising , 1995 .
[31] Balas K. Natarajan,et al. Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..
[32] Shor,et al. Good quantum error-correcting codes exist. , 1995, Physical review. A, Atomic, molecular, and optical physics.
[33] Ronald A. DeVore,et al. Some remarks on greedy algorithms , 1996, Adv. Comput. Math..
[34] Gene H. Golub,et al. Matrix computations (3rd ed.) , 1996 .
[35] Fadil Santosa,et al. Recovery of Blocky Images from Noisy and Blurred Data , 1996, SIAM J. Appl. Math..
[36] C. Burrus,et al. Noise reduction using an undecimated discrete wavelet transform , 1996, IEEE Signal Processing Letters.
[37] David J. Field,et al. Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.
[38] Edward H. Adelson,et al. Noise removal via Bayesian wavelet coring , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.
[39] Steane,et al. Simple quantum error-correcting codes. , 1996, Physical review. A, Atomic, molecular, and optical physics.
[40] D. Field,et al. Natural image statistics and efficient coding. , 1996, Network.
[41] Ronald R. Coifman,et al. Brushlets: A Tool for Directional Image Analysis and Image Compression , 1997 .
[42] Bhaskar D. Rao,et al. Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm , 1997, IEEE Trans. Signal Process..
[43] David J. Field,et al. Sparse coding with an overcomplete basis set: A strategy employed by V1? , 1997, Vision Research.
[44] S. Mallat,et al. Adaptive greedy approximations , 1997 .
[45] I. Johnstone,et al. Minimax estimation via wavelet shrinkage , 1998 .
[46] Michael A. Saunders,et al. Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..
[47] Martin Vetterli,et al. Spatially adaptive wavelet thresholding with context modeling for image denoising , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).
[48] S. Mallat. A wavelet tour of signal processing , 1998 .
[49] Eero P. Simoncelli,et al. Image compression via joint statistical characterization in the wavelet domain , 1999, IEEE Trans. Image Process..
[50] H. Sebastian Seung,et al. Learning the parts of objects by non-negative matrix factorization , 1999, Nature.
[51] R. DeVore,et al. Nonlinear Approximation and the Space BV(R2) , 1999 .
[52] Pierre Moulin,et al. Analysis of Multiresolution Image Denoising Schemes Using Generalized Gaussian and Complexity Priors , 1999, IEEE Trans. Inf. Theory.
[53] Xiaoming Huo,et al. Sparse image representation via combined transforms , 1999 .
[54] Bhaskar D. Rao,et al. An affine scaling methodology for best basis selection , 1999, IEEE Trans. Signal Process..
[55] Bruno A. Olshausen,et al. PROBABILISTIC FRAMEWORK FOR THE ADAPTATION AND COMPARISON OF IMAGE CODES , 1999 .
[56] Martin Vetterli,et al. Adaptive wavelet thresholding for image denoising and compression , 2000, IEEE Trans. Image Process..
[57] Martin Vetterli,et al. Wavelet thresholding for multiple noisy image copies , 2000, IEEE Trans. Image Process..
[58] Terrence J. Sejnowski,et al. Learning Overcomplete Representations , 2000, Neural Computation.
[59] Barak A. Pearlmutter,et al. Blind source separation by sparse decomposition , 2000, SPIE Defense + Commercial Sensing.
[60] Kjersti Engan,et al. Multi-frame compression: theory and design , 2000, Signal Process..
[61] Yoram Bresler,et al. On the Optimality of the Backward Greedy Algorithm for the Subset Selection Problem , 2000, SIAM J. Matrix Anal. Appl..
[62] Paul Tseng,et al. Block coordinate relaxation methods for nonparametric signal denoising with wavelet dictionaries , 2000 .
[63] Amir Averbuch,et al. Fast adaptive wavelet packet image compression , 2000, IEEE Trans. Image Process..
[64] M. R. Osborne,et al. A new approach to variable selection in least squares problems , 2000 .
[65] P. Tseng,et al. Block Coordinate Relaxation Methods for Nonparametric Wavelet Denoising , 2000 .
[66] Vladimir N. Temlyakov,et al. Weak greedy algorithms[*]This research was supported by National Science Foundation Grant DMS 9970326 and by ONR Grant N00014‐96‐1‐1003. , 2000, Adv. Comput. Math..
[67] Trevor Hastie,et al. The Elements of Statistical Learning , 2001 .
[68] Maarten Jansen,et al. Noise Reduction by Wavelet Thresholding , 2001 .
[69] Xiaoming Huo,et al. Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.
[70] Nikos D. Sidiropoulos,et al. Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays , 2001, IEEE Trans. Signal Process..
[71] Emmanuel J. Candès,et al. The curvelet transform for image denoising , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).
[72] Barak A. Pearlmutter,et al. Blind Source Separation by Sparse Decomposition in a Signal Dictionary , 2001, Neural Computation.
[73] Erkki Oja,et al. Independent Component Analysis , 2001 .
[74] Michael Elad,et al. A generalized uncertainty principle and sparse representation in pairs of bases , 2002, IEEE Trans. Inf. Theory.
[75] E. Candès,et al. Recovering edges in ill-posed inverse problems: optimality of curvelet frames , 2002 .
[76] Minh N. Do,et al. Rotation invariant texture characterization and retrieval using steerable wavelet-domain hidden Markov models , 2002, IEEE Trans. Multim..
[77] P. Laguna,et al. Signal Processing , 2002, Yearbook of Medical Informatics.
[78] Michael W. Marcellin,et al. JPEG2000 - image compression fundamentals, standards and practice , 2002, The Kluwer International Series in Engineering and Computer Science.
[79] Ronald R. Coifman,et al. Multilayered image representation: application to image compression , 2002, IEEE Trans. Image Process..
[80] Brendt Wohlberg,et al. Noise sensitivity of sparse signal representations: reconstruction error bounds for the inverse problem , 2003, IEEE Trans. Signal Process..
[81] Minh N. Do,et al. The finite ridgelet transform for image representation , 2003, IEEE Trans. Image Process..
[82] Michael Elad,et al. Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.
[83] Robert D. Nowak,et al. An EM algorithm for wavelet-based image restoration , 2003, IEEE Trans. Image Process..
[84] Joseph F. Murray,et al. Dictionary Learning Algorithms for Sparse Representation , 2003, Neural Computation.
[85] S. Muthukrishnan,et al. Approximation of functions over redundant dictionaries using coherence , 2003, SODA '03.
[86] I. Daubechies,et al. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.
[87] Martin J. Wainwright,et al. Image denoising using scale mixtures of Gaussians in the wavelet domain , 2003, IEEE Trans. Image Process..
[88] Thomas Strohmer,et al. GRASSMANNIAN FRAMES WITH APPLICATIONS TO CODING AND COMMUNICATION , 2003, math/0301135.
[89] R. Eslami,et al. The contourlet transform for image denoising using cycle spinning , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.
[90] S. Muthukrishnan,et al. Improved sparse approximation over quasiincoherent dictionaries , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).
[91] Rémi Gribonval,et al. Sparse representations in unions of bases , 2003, IEEE Trans. Inf. Theory.
[92] Bhaskar D. Rao,et al. Subset selection in noise based on diversity measure minimization , 2003, IEEE Trans. Signal Process..
[93] Minh N. Do,et al. Framing pyramids , 2003, IEEE Trans. Signal Process..
[94] Victoria Stodden,et al. When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts? , 2003, NIPS.
[95] Arkadi Nemirovski,et al. On sparse representation in pairs of bases , 2003, IEEE Trans. Inf. Theory.
[96] R. Tibshirani,et al. Least angle regression , 2004, math/0406456.
[97] Joel A. Tropp,et al. Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.
[98] Jean-Jacques Fuchs,et al. On sparse representations in arbitrary redundant bases , 2004, IEEE Transactions on Information Theory.
[99] Venkat Chandrasekaran,et al. Surflets: a sparse representation for multidimensional functions containing smooth discontinuities , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..
[100] E. Candès,et al. New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities , 2004 .
[101] Dmitry M. Malioutov,et al. Optimal sparse representations in general overcomplete bases , 2004, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing.
[102] Yuanqing Li,et al. Analysis of Sparse Representation and Blind Source Separation , 2004, Neural Computation.
[103] Patrik O. Hoyer,et al. Non-negative Matrix Factorization with Sparseness Constraints , 2004, J. Mach. Learn. Res..
[104] D. Donoho,et al. Redundant Multiscale Transforms and Their Application for Morphological Component Separation , 2004 .
[105] J. Tropp. JUST RELAX: CONVEX PROGRAMMING METHODS FOR SUBSET SELECTION AND SPARSE APPROXIMATION , 2004 .
[106] Kannan Ramchandran,et al. Analysis of denoising by sparse approximation with random frame asymptotics , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..
[107] Minh N. Do,et al. Ieee Transactions on Image Processing the Contourlet Transform: an Efficient Directional Multiresolution Image Representation , 2022 .
[108] Rémi Gribonval,et al. Learning unions of orthonormal bases with thresholded singular value decomposition , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..
[109] Dmitry M. Malioutov,et al. A sparse signal reconstruction perspective for source localization with sensor arrays , 2005, IEEE Transactions on Signal Processing.
[110] Jean-Jacques Fuchs,et al. Recovery of exact sparse representations in the presence of bounded noise , 2005, IEEE Transactions on Information Theory.
[111] Emmanuel Candes,et al. Stable signal recovery from incomplete observations , 2005, SPIE Optics + Photonics.
[112] Mark D. Plumbley. Geometry and homotopy for l 1 sparse representations , 2005 .
[113] S. Mendelson,et al. Reconstruction and subgaussian processes , 2005 .
[114] Stéphane Mallat,et al. Sparse geometric image representations with bandelets , 2005, IEEE Transactions on Image Processing.
[115] Robert D. Nowak,et al. A bound optimization approach to wavelet-based image deconvolution , 2005, IEEE International Conference on Image Processing 2005.
[116] E. Candès,et al. Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.
[117] Michael Elad,et al. Submitted to Ieee Transactions on Image Processing Image Decomposition via the Combination of Sparse Representations and a Variational Approach , 2022 .
[118] Stéphane Mallat,et al. Bandelet Image Approximation and Compression , 2005, Multiscale Model. Simul..
[119] F. Lemmermeyer. Error-correcting Codes , 2005 .
[120] Justin Romberg,et al. Practical Signal Recovery from Random Projections , 2005 .
[121] Michael Elad,et al. K-SVD and its non-negative variant for dictionary design , 2005, SPIE Optics + Photonics.
[122] Emmanuel J. Candès,et al. Decoding by linear programming , 2005, IEEE Transactions on Information Theory.
[123] D. Donoho,et al. Neighborliness of randomly projected simplices in high dimensions. , 2005, Proceedings of the National Academy of Sciences of the United States of America.
[124] D. Donoho,et al. Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA) , 2005 .
[125] D. Donoho,et al. Sparse nonnegative solution of underdetermined linear equations by linear programming. , 2005, Proceedings of the National Academy of Sciences of the United States of America.
[126] M. Rudelson,et al. Geometric approach to error-correcting codes and reconstruction of signals , 2005, math/0502299.
[127] A. Bruckstein,et al. K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .
[128] Michael Lustig,et al. k-t SPARSE: High frame rate dynamic MRI exploiting spatio-temporal sparsity , 2006 .
[129] Michael Elad,et al. Image Denoising Via Learned Dictionaries and Sparse representation , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).
[130] Yaakov Tsaig,et al. Extensions of compressed sensing , 2006, Signal Process..
[131] José M. Bioucas-Dias,et al. Bayesian wavelet-based image deconvolution: a GEM algorithm exploiting a class of heavy-tailed priors , 2006, IEEE Transactions on Image Processing.
[132] Kannan Ramchandran,et al. Denoising by Sparse Approximation: Error Bounds Based on Rate-Distortion Theory , 2006, EURASIP J. Adv. Signal Process..
[133] Michael Elad,et al. Image Denoising with Shrinkage and Redundant Representations , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).
[134] Pierre Vandergheynst,et al. A simple test to check the optimality of a sparse signal approximation , 2006, Signal Process..
[135] D. Donoho. For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution , 2006 .
[136] D. Donoho. For most large underdetermined systems of equations, the minimal 𝓁1‐norm near‐solution approximates the sparsest near‐solution , 2006 .
[137] Michael Elad,et al. Why Simple Shrinkage Is Still Relevant for Redundant Representations? , 2006, IEEE Transactions on Information Theory.
[138] S. Mendelson,et al. Uniform Uncertainty Principle for Bernoulli and Subgaussian Ensembles , 2006, math/0608665.
[139] Michael Elad. Sparse Representations Are Most Likely to Be the Sparsest Possible , 2006, EURASIP J. Adv. Signal Process..
[140] Emmanuel J. Candès,et al. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.
[141] Hayder Radha,et al. Translation-Invariant Contourlet Transform and Its Application to Image Denoising , 2006, IEEE Transactions on Image Processing.
[142] Michael Elad,et al. Stable recovery of sparse overcomplete representations in the presence of noise , 2006, IEEE Transactions on Information Theory.
[143] Michael Elad,et al. Morphological diversity and source separation , 2006, IEEE Signal Processing Letters.
[144] M. Elad,et al. $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.
[145] Onur G. Guleryuz,et al. Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising-part I: theory , 2006, IEEE Transactions on Image Processing.
[146] Emmanuel J. Candès,et al. Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions , 2004, Found. Comput. Math..
[147] David L Donoho,et al. Compressed sensing , 2006, IEEE Transactions on Information Theory.
[148] Michael Elad,et al. On the stability of the basis pursuit in the presence of noise , 2006, Signal Process..
[149] David L. Donoho,et al. Sparse Solution Of Underdetermined Linear Equations By Stagewise Orthogonal Matching Pursuit , 2006 .
[150] Jean-Luc Starck,et al. Sparse Representation-based Image Deconvolution by iterative Thresholding , 2006 .
[151] Onur G. Guleryuz,et al. Nonlinear approximation based image recovery using adaptive sparse reconstructions and iterated denoising-part II: adaptive algorithms , 2006, IEEE Transactions on Image Processing.
[152] Pierre Vandergheynst,et al. On the exponential convergence of matching pursuits in quasi-incoherent dictionaries , 2006, IEEE Transactions on Information Theory.
[153] Michael Elad,et al. Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.
[154] Yaakov Tsaig,et al. Breakdown of equivalence between the minimal l1-norm solution and the sparsest solution , 2006, Signal Process..
[155] Mark D. Plumbley. Recovery of Sparse Representations by Polytope Faces Pursuit , 2006, ICA.
[156] J. Fadili,et al. SZ and CMB reconstruction using generalized morphological component analysis , 2007, 0712.0588.
[157] A. Bruckstein,et al. On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them , 2006 .
[158] Robert D. Nowak,et al. Majorization–Minimization Algorithms for Wavelet-Based Image Restoration , 2007, IEEE Transactions on Image Processing.
[159] Mark D. Plumbley. On Polar Polytopes and the Recovery of Sparse Representations , 2007, IEEE Trans. Inf. Theory.
[160] Michael Elad,et al. Cross-Modal Localization via Sparsity , 2007, IEEE Transactions on Signal Processing.
[161] Mohamed-Jalal Fadili,et al. The Undecimated Wavelet Decomposition and its Reconstruction , 2007, IEEE Transactions on Image Processing.
[162] Michael Elad,et al. Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization , 2007 .
[163] Joel A. Tropp,et al. Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.
[164] D. Donoho,et al. Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.
[165] Michael Elad,et al. Compression of facial images using the K-SVD algorithm , 2008, J. Vis. Commun. Image Represent..
[166] A. Barron,et al. Approximation and learning by greedy algorithms , 2008, 0803.1718.
[167] Michael Elad,et al. Sparse Representation for Color Image Restoration , 2008, IEEE Transactions on Image Processing.
[168] Michael Elad,et al. Image Sequence Denoising via Sparse and Redundant Representations , 2009, IEEE Transactions on Image Processing.
[169] I. Kozlov,et al. Sparse Solutions of Underdetermined Linear Systems , 2015 .
[170] R. DeVore,et al. Nonlinear approximation and the space BV[inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] , 1999 .