Iteratively Reweighted ℓ1 Minimization with Nonzero Index Update

Abstract

The acquisition of a discrete-time signal is an important part of compressive sensing. Instead of ℓ0-norm optimization, much attention is paid to ℓ1-norm problem formulation due to its computability at comparable accuracy. Iteratively reweighted ℓ1 (IRL1) minimization is known to be an improved algorithm of typical ℓ1-norm criterion. In this work, an alternative enhancement of the IRL1-norm criterion is presented. The proposed method invokes a descending sort of the absolute values of all elements in the solution and updates the nonzero indices in each iteration without any additional matrix factorization and matrix inverse. Numerical examples illustrate that for a large number of nonzero elements in the data the proposed nonzero index update can help the IRL1 minimization to perform noticeably better.