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Communication Dans Un Congrès Année : 2003

Sparse Decompositions in ``incoherent'' dictionaries

Résumé

The purpose of this paper is to generalize a result by Donoho, Huo, Elad and Bruckstein on sparse representations of signals/images in a union of two orthonormal bases. We consider general (redundant) dictionaries in finite dimension, and derive sufficient conditions on a signal/image for having a unique sparse representation in such a dictionary. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of a combinatorial optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may he highly redundant. The special case where the dictionary is given by a union of several orthonormal bases is studied in more detail and some examples are given.
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Dates et versions

inria-00570099 , version 1 (26-02-2011)

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Rémi Gribonval, Morten Nielsen. Sparse Decompositions in ``incoherent'' dictionaries. Proc. IEEE Intl. Conf. Image Proc. (ICIP'03), Sep 2003, Barcelona, Spain. pp.I-33 -- I-36, ⟨10.1109/ICIP.2003.1246891⟩. ⟨inria-00570099⟩
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