On sparse representation in pairs of bases
IEEE Transactions on Information TheoryPublished 29 May 2003
Arie Feuer, Arkadi Nemirovski
Citations164
SJR quartileQ1
SJR score1.46
SNIP1.76
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TL;DR
It is established here that the EB condition is both sufficient and necessary for replacing an l/sub 0/ optimization by linear programming minimization when searching for the unique sparse representation.
Abstract
In previous work, Elad and Bruckstein (EB) have provided a sufficient condition for replacing an l/sub 0/ optimization by linear programming minimization when searching for the unique sparse representation. We establish here that the EB condition is both sufficient and necessary.
Keywords
Computer ScienceEngineering
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It is proved that if S is representable as a highly sparse superposition of atoms from this time-frequency dictionary, then there is only one such highly sparse representation of S, and it can be obtained by solving the convex optimization problem of minimizing the l/sup 1/ norm of the coefficients among all decompositions.
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The main contribution in this paper is the improvement of an important result due to Donoho and Huo (2001) concerning the replacement of the l/sub 0/ optimization problem by a linear programming minimization when searching for the unique sparse representation.
