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Sparse decomposition over multi-component redundant dictionaries

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2 Author(s)
Granai, L. ; Signal Process. Inst., Swiss Federal Inst. of Technol., Lausanne, Switzerland ; Vandergheynst, P.

In many applications - such as compression, de-noising and source separation - a good and efficient signal representation is characterized by sparsity. This means that many coefficients are close to zero, while only few ones have a non-negligible amplitude. On the other hand, real-world signals such as audio or natural images - clearly present peculiar structures. In this paper we introduce a global optimization framework that aims at respecting the sparsity criterion while decomposing a signal over an overcomplete, multi-component dictionary. We adopt a probabilistic analysis which can lead to consider the signal internal structure. As an example that fits this framework, we propose the weighted basis pursuit algorithm, based on the solution of a convex, non-quadratic problem. Results show that this method can provide sparse signal representations and sparse m-terms approximations. Moreover, weighted basis pursuit provides a faster convergence compared to basis pursuit.

Published in:

Multimedia Signal Processing, 2004 IEEE 6th Workshop on

Date of Conference:

29 Sept.-1 Oct. 2004