Publications Journal Papers

Sparse Representation Theory

D. Simon, J. Sulam, Y. Romano, Y.M. Lu, and M. Elad, MMSE Approximation For Sparse Coding Algorithms Using Stochastic Resonance, IEEE Transactions on Signal Processing, Vol. 67, No. 17, Pages 4597-4610, September 2019.
Y. Yankelevsky and M. Elad, Theoretical Guarantees for Graph Sparse Coding, Applied Computational Harmonic Analysis, April 2019.
J. Sulam, A. Aberdam, A. Beck, and M. Elad, On Multi-Layer Basis Pursuit, Efficient Algorithms and Convolutional Neural Networks, IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), March 2019.
A. Aberdam, J. Sulam, and M. Elad, Multi Layer Sparse Coding: the Holistic Way, SIAM Journal on Mathematics of Data Science (SIMODS), Vol. 1, No. 1, Pages 46-77, February 2019. software
Y. Romano, A. Aberdam, J. Sulam, and M. Elad, Adversarial Noise Attacks of Deep Learning Architectures – Stability Analysis via Sparse Modeled Signals, to appear in Journal of Mathematical Imaging and Vision (Special issue on Mathematical Foundations of Deep Learning in Imaging Sciences).
J. Sulam, V. Papyan, Y. Romano, and M. Elad, Multi-Layer Convolutional Sparse Modeling: Pursuit and Dictionary Learning, IEEE Trans. on Signal Processing, Vol. 66, No. 15, Pages 4090-4104, August 2018.
V. Papyan, Y. Romano, J. Sulam, and M. Elad, Theoretical Foundations of Deep Learning via Sparse Representations, IEEE Signal Processing Magazine, Vol. 35, No. 4, Pages 72-89, June 2018.
V. Papyan, J. Sulam, and M. Elad, Working Locally Thinking Globally: Theoretical Guarantees for Convolutional Sparse Coding, IEEE Trans. on Signal Processing, Vol. 65, No. 21, Pages 5687-5701, November 2017.
V. Papyan, Y. Romano, and M. Elad, Convolutional Neural Networks Analyzed via Convolutional Sparse Coding, Journal of Machine Learning Research, Vol. 18, Pages 1-52, July 2017.
R. Giryes, M. Elad, and A.M. Bruckstein, Sparsity Based Methods for Overparameterized Variational Problems, SIAM Journal on Imaging Sciences, Vol. 8, No. 3, Pages 2133-2159, November 2015.
J.S. Turek, I. Yavneh, and M. Elad, On MAP and MMSE Estimators for the Co-sparse Analysis Model, Elsevier Digital Signal Processing, Vol. 28, Pages 57-74, May 2014.
R. Giryes, S. Nam, M. Elad, R.Gribonval, and M.E. Davies, Greedy-Like Algorithms for the Cosparse Analysis Model, Linear Algebra and Applications, Vol. 441, Pages 22-60, January 2014.
T. Peleg and M. Elad, Performance Guarantees of the Thresholding Algorithm for the Co-Sparse Analysis Model, IEEE Trans. on Information Theory, Vol. 59, No. 3, Pages 1832-1845, March 2013.
M. Elad, Sparse and Redundant Representation Modeling — What Next?, IEEE Signal Processing Letters, Vol. 19, No. 12, Pages 922-928, December 2012.
T. Peleg, Y.C. Eldar, and M. Elad, Exploiting Statistical Dependencies in Sparse Representations for Signal Recovery, IEEE Trans. on Signal Processing, Vol. 60, No. 5, Pages 2286-2303, May 2012. software
R. Giryes and M. Elad, RIP-Based Near-Oracle Performance Guarantees for Subspace-Pursuit, CoSaMP, oland Iterative Hard-Threshding, IEEE Trans. on Signal Processing, Vol. 60, No. 3, Pages 1465 - 1468, March 2012.
S. Nam, M.E. Davies, M. Elad, and R. Gribonval, The Cosparse Analysis Model and Algorithms, Applied and Computational Harmonic Analysis, Vol. 34, No. 1, Pages 30-56, January 2013.
J.S. Turek, I. Yavneh, and M. Elad, On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary Dictionary, IEEE Transactions on Signal Processing, Vol. 59, No. 8, Pages 3526-3535, August 2011.
Z. Ben-Haim, Y.C. Eldar, and M. Elad, Coherence-Based Performance Guarantees for Estimating a Sparse Vector Under Random Noise, IEEE Transactions on Signal Processing, Vol. 58, No. 10, Pages 5030-5043, October 2010.
M. Protter, I. Yavneh, and M. Elad, Closed-Form MMSE Estimation for Signal Denoising Under Sparse Representation Modelling Over a Unitary Dictionary, IEEE Transactions on Signal Processing, Vol. 58, No. 7, Pages 3471-3484, July 2010.
M. Elad, M.A.T. Figueiredo, and Y. Ma, On the Role of Sparse and Redundant Representations in Image Processing, IEEE Proceedings - Special Issue on Applications of Sparse Representation & Compressive Sensing, Vol. 98, No. 6, Pages 972-982, April 2010.
M. Elad and I. Yavneh, A Plurality of Sparse Representations is Better Than the Sparsest One Alone, IEEE Transactions on Information Theory, Vol. 55, No. 10, Pages 4701-4714, October 2009.
A.M. Bruckstein, D.L. Donoho, and M. Elad, From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images, SIAM Review, Vol. 51, No. 1, Pages 34-81, February 2009.
J. Shtok and M. Elad, Analysis of the Basis Pursuit Via the Capacity Sets, Journal of Fourier Analysis and Applications, Vol. 14, No. 5-6, Pages: 688-711, December 2008.
A.M. Bruckstein, M. Elad, and M. Zibulevsky, A Non-Negative and Sparse Enough Solution of an Underdetermined Linear System of Equations is Unique, IEEE Transactions on Information Theory, Vol. 54, No. 11, Pages 4813-4820, November 2008.
D.L. Donoho, M. Elad, and V.N. Temlyakov, On Lebesgue-Type Inequalities for Greedy Approximation, Journal of Approximation Theory, Vol. 147, No. 2, Pages 185-195, August 2007.
M. Elad, P. Milanfar, and R. Rubinstein, Analysis Versus Synthesis in Signal Priors, Inverse Problems. Vol. 23, no. 3, Pages 947-968, June 2007.
M. Elad, Why Simple Shrinkage is Still Relevant for Redundant Representations?, IEEE Trans. On Information Theory, Vol. 52, no. 12, pp. 5559-5569, December 2006. software
D.L. Donoho and M. Elad, On the Stability of the Basis Pursuit in the Presence of Noise, EURASIP Signal Processing Journal, Vol. 86, No. 3, pp. 511-532, March 2006. software
M. Elad, Sparse Representations are Most Likely to be the Sparsest Possible, the Journal on Applied Signal Processing, Vol. 2006, pp. 1-12, 2006.
D.L. Donoho, M. Elad, and V. Temlyakov, Stable Recovery of Sparse Overcomplete Representations in the Presence of Noise, the IEEE Trans. On Information Theory, Vol. 52, pp. 6-18, January 2006. software
D. L. Donoho and M. Elad, Optimally Sparse Representation in General (nonorthogonal) Dictionaries via L1 Minimization, the Proc. Nat. Aca. Sci., Vol. 100, pp. 2197-2202, March 2003.
M. Elad and A.M. Bruckstein, A Generalized Uncertainty Principle and Sparse Representation in Pairs of Bases, IEEE Trans. On Information Theory, Vol. 48, pp. 2558-2567, September 2002.
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