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• W1981487911 abstract "Numerical experiments have indicated that the reweighted $ell_1$-minimization performs exceptionally well in locating sparse solutions of underdetermined linear systems of equations. We show that reweighted $ell_1$-methods are intrinsically associated with the minimization of the so-called merit functions for sparsity, which are essentially concave approximations to the cardinality function. Based on this observation, we further show that a family of reweighted $ell_1$-algorithms can be systematically derived from the perspective of concave optimization through the linearization technique. In order to conduct a unified convergence analysis for this family of algorithms, we introduce the concept of the range space property (RSP) of a matrix and prove that if its adjoint has this property, the reweighted $ell_1$-algorithm can find a sparse solution to the underdetermined linear system provided that the merit function for sparsity is properly chosen. In particular, some convergence conditions for the Candès--Wakin--Boyd method and the recent $ell_p$-quasi-norm-based reweighted $ell_1$-method can be obtained as special cases of the general framework." @default.
• W1981487911 created "2016-06-24" @default.
• W1981487911 creator A5057733991 @default.
• W1981487911 creator A5071703782 @default.
• W1981487911 date "2012-01-01" @default.
• W1981487911 modified "2023-10-01" @default.
• W1981487911 title "Reweighted $ell_1$-Minimization for Sparse Solutions to Underdetermined Linear Systems" @default.
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• W1981487911 doi "https://doi.org/10.1137/110847445" @default.
• W1981487911 hasPublicationYear "2012" @default.
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