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Sparse representations in unions of bases | IEEE Journals & Magazine | IEEE Xplore

Sparse representations in unions of bases


Abstract:

The purpose of this correspondence is to generalize a result by Donoho and Huo and Elad and Bruckstein on sparse representations of signals in a union of two orthonormal ...Show More

Abstract:

The purpose of this correspondence is to generalize a result by Donoho and Huo and Elad and Bruckstein on sparse representations of signals in a union of two orthonormal bases for R/sup N/. We consider general (redundant) dictionaries for R/sup N/, and derive sufficient conditions for having unique sparse representations of signals in such dictionaries. The special case where the dictionary is given by the union of L/spl ges/2 orthonormal bases for R/sup N/ is studied in more detail. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of the /spl lscr//sup 0/ optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may be highly redundant.
Published in: IEEE Transactions on Information Theory ( Volume: 49, Issue: 12, December 2003)
Page(s): 3320 - 3325
Date of Publication: 07 January 2004

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