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Reports (Research Report) Year : 2002

Sparse Representations in Unions of Bases


The purpose of this paper is to generalize a result by Donoho, Huo, Elad and Bruckstein on sparse representations of signals in a union of two orthonormal bases. We consider general (redundant) dictionaries in finite dimension, and derive sufficient conditions on a signal for having unique sparse representations in such dictionaries. The special case where the dictionary is given by a union of several orthonormal bases is studied in more detail. 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 be highly redundant.
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Dates and versions

inria-00071943 , version 1 (23-05-2006)


  • HAL Id : inria-00071943 , version 1


Rémi Gribonval, Morten Nielsen. Sparse Representations in Unions of Bases. [Research Report] RR-4642, INRIA. 2002. ⟨inria-00071943⟩
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