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A Biconvex Analysis for Lasso - Reweighting | IEEE Journals & Magazine | IEEE Xplore

A Biconvex Analysis for Lasso \ell _1 Reweighting


Abstract:

Iterative l1 reweighting algorithms are very popular in sparse signal recovery and compressed sensing, since in the practice they have been observed to outperform classic...Show More

Abstract:

Iterative l1 reweighting algorithms are very popular in sparse signal recovery and compressed sensing, since in the practice they have been observed to outperform classical 11 methods. Nevertheless, the theoretical analysis of their convergence is a critical point, and generally is limited to the convergence of the functional to a local minimum or to subsequence convergence. In this letter, we propose a new convergence analysis of a Lasso l1 reweighting method, based on the observation that the algorithm is an alternated convex search for a biconvex problem. Based on that, we are able to prove the numerical convergence of the sequence of the iterates generated by the algorithm. Furthermore, we propose an alternative iterative soft thresholding procedure, which is faster than the main algorithm.
Published in: IEEE Signal Processing Letters ( Volume: 25, Issue: 12, December 2018)
Page(s): 1795 - 1799
Date of Publication: 10 October 2018

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