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The purpose of this paper is to extend results by Villemoes about exponential convergence of Matching Pursuit with some structured dictionaries for simple functions in finite or infinite dimension. Our results are based on an extension of Tropps results ...
There is a growing interest on adapted signal expansions for efficient sparse approximations. For this purpose, signal expansions on over-complete bases are of high interest. Several strategies exist in order to get sparse approximations of a signal as a s ...
This paper presents a new image representation method based on anisotropic refinement. It has been shown that wavelets are not optimal to code 2-D objects which need true 2-D dictionaries for efficient approximation. We propose to use rotations and anisotr ...
This report studies the effect of introducing a priori knowledge to recover sparse representations when overcomplete dictionaries are used. We focus mainly on Greedy algorithms and Basis Pursuit as for our algorithmic basement, while a priori is incorporat ...
The matching pursuit algorithm can be used to derive signal decompositions in terms of the elements of a dictionary of time-frequency atoms. Using a structured overcomplete dictionary yields a signal model that is both parametric and signal-adaptive. In th ...
Compression efficiency is mainly driven by redundancy of the overcomplete set of functions chosen for the signal decomposition. In Matching Pursuit algorithms for example, the redundancy of the dictionary influences the convergence of the residual energy. ...
