Computation and relaxation of conditions for equivalence between ℓ 1 and ℓ 0 minimization,” CSL (2007)
| Citations: | 5 - 3 self |
BibTeX
@TECHREPORT{Sharon07computationand,
author = {Yoav Sharon and Student Member and John Wright and Student Member and Yi Ma and Senior Member},
title = {Computation and relaxation of conditions for equivalence between ℓ 1 and ℓ 0 minimization,” CSL},
institution = {},
year = {2007}
}
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Abstract
Abstract—In this paper, we investigate the exact conditions under which the ℓ 1 and ℓ 0 minimizations arising in the context of sparse error correction or sparse signal reconstruction are equivalent. We present a much simplified condition for verifying equivalence, which leads to a provably correct algorithm that computes the exact sparsity of the error or the signal needed to ensure equivalence. In the case when the encoding matrix is imbalanced, we show how an optimal diagonal rescaling matrix can be computed via linear programming, so that the rescaled system enjoys the widest possible equivalence. I.
