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The K-SVD algorithm is a highly effective method of training overcomplete dictionaries for sparse signal representation. In this report we discuss an efficient implementation of this algorithm, which both accelerates it and reduces its memory consumption. The two basic components of our implementation are the replacement of the exact SVD computation with a… (More)

- Michael Zibulevsky, Barak A. Pearlmutter
- Neural Computation
- 2001

The blind source separation problem is to extract the underlying source signals from a set of linear mixtures, where the mixing matrix is unknown. This situation is common in acoustics, radio, medical signal and image processing, hyperspectral imaging, and other areas. We suggest a two-stage separation process: a priori selection of a possibly overcomplete… (More)

- Pau Bofill, Michael Zibulevsky
- Signal Processing
- 2001

- Ron Rubinstein, Michael Zibulevsky, Michael Elad
- IEEE Transactions on Signal Processing
- 2010

An efficient and flexible dictionary structure is proposed for sparse and redundant signal representation. The proposed sparse dictionary is based on a sparsity model of the dictionary atoms over a base dictionary, and takes the form D = ¿ A, where ¿ is a fixed base dictionary and A is sparse. The sparse dictionary provides efficient forward and adjoint… (More)

- Michael Zibulevsky, Michael Elad
- IEEE Signal Processing Magazine
- 2010

Sparse, redundant representations offer a powerful emerging model for signals. This model approximates a data source as a linear combination of few atoms from a prespecified and over-complete dictionary. Often such models are fit to data by solving mixed ¿<sub>1</sub>-¿<sub>2</sub> convex optimization problems. Iterative-shrinkage algorithms constitute a… (More)

This work addresses the problem of regularized linear least squares (RLS) with non-quadratic separable regularization. Despite being frequently deployed in many applications, the RLS problem is often hard to solve using standard iterative methods. In a recent work [10], a new iterative method called Parallel Coordinate Descent (PCD) was devised. We provide… (More)

- Alfred M. Bruckstein, Michael Elad, Michael Zibulevsky
- IEEE Transactions on Information Theory
- 2008

An underdetermined linear system of equations <i>Ax</i> = <i>b</i> with nonnegativity constraint <i>x</i> ges 0 is considered. It is shown that for matrices <i>A</i> with a row-span intersecting the positive orthant, if this problem admits a sufficiently sparse solution, it is necessarily unique. The bound on the required sparsity depends on a coherence… (More)

- Aharon Ben-Tal, Michael Zibulevsky
- SIAM Journal on Optimization
- 1997

We study a class of methods for solving convex programs, which are based on nonquadratic Augmented Lagrangians for which the penalty parameters are functions of the multipliers. This gives rise to lagrangians which are nonlinear in the multipliers. Each augmented lagrangian is speciied by a choice of a penalty function ' and a penalty-updating function. The… (More)

- M Elad, B Matalon, J Shtok, M Zibulevsky
- 2007

Sparse and redundant representations – an emerging and powerful model for signals – suggests that a data source could be described as a linear combination of few atoms from a pre-specified and over-complete dictionary. This model has drawn a considerable attention in the past decade, due to its appealing theoretical foundations, and promising practical… (More)

- Alexander M. Bronstein, Michael M. Bronstein, Michael Zibulevsky, Yehoshua Y. Zeevi
- Int. J. Imaging Systems and Technology
- 2005

We address the problem of recovering a scene recorded through a semireflecting medium (i.e. planar lens), with a virtual reflected image being superimposed on the image of the scene transmitted through the semirefelecting lens. Recent studies propose imaging through a linear polarizer at several orientations to estimate the reflected and the transmitted… (More)