Parametric Dictionary Design for Sparse Coding

Abstract : This paper introduces a new dictionary design method for sparse coding of a class of signals. It has been shown that one can sparsely approximate some natural signals using an overcomplete set of parametric functions, e.g. [1], [2]. A problem in using these parametric dictionaries is how to choose the parameters. In practice these parameters have been chosen by an expert or through a set of experiments. In the sparse approximation context, it has been shown that an incoherent dictionary is appropriate for the sparse approximation methods. In this paper we first characterize the dictionary design problem, subject to a minimum coherence constraint. Then we briefly explain that equiangular tight frames have minimum coherence. The parametric dictionary design is then to find an admissible dictionary close to being tight frame. The complexity of the problem does not allow it to be solved exactly. We introduce a practical method to approximately solve it. Some experiments show the advantages one gets by using these dictionaries. Index Terms—Sparse Approximation, Dictionary Design, Incoherent Dictionary, Parametric Dictionary, Gammatone Filter Banks, Exact Sparse Recovery.
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Conference papers
Rémi Gribonval. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Apr 2009, Saint Malo, France. 2009
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Mehrdad Yaghoobi, Laurent Daudet, Mike E. Davies. Parametric Dictionary Design for Sparse Coding. Rémi Gribonval. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Apr 2009, Saint Malo, France. 2009. 〈inria-00369364〉

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