Efficient backward elimination algorithm for sparse signal representation using overcomplete dictionaries

Abstract

A sparse representation of a signal, i.e., a representation using a small number of vectors chosen from a dictionary of vectors, is highly desirable in many applications. Here, we extend the backward elimination sparse representation algorithm presented in [1] to allow for an overcomplete dictionary and develop recursions for its implementation. In the overcomplete case, the representation error cannot be used as a general criterion for elimination of a dictionary vector and other criteria must be considered. Simulation on a test-case dictionary shows that the performance of the proposed algorithm can improve upon that of forward selection methods.Index Terms-Backward elimination algorithm, overcomplete dictionary, sparse representation, subset selection.

Source localization using a sparse representation framework to achieve superresolution

“…Sparse representation, or sparse coding, of signals has received a lot of attention in recent years (e.g., Cotter et al 2002;Gorodnitsky and Rao 1997). One important application of this signal model is in source localization.…”

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