Iteratively Reweighted Least Squares Minimization with Nonzero Index Update

Abstract

The acquisition of a discrete-time signal is an important part in compressive sensing problem. Instead of using l0-norm optimization, much attention is paid to lp-norm formulation for p ? (0,1) due to its fast convergence and comparable accuracy. Iteratively reweighted least squares (IRLS) minimization is known as an improved algorithm of the typical basis pursuit with l1-norm criterion. In this work, an alternative enhancement of the IRLS 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. Numerical examples illustrate that the proposed nonzero index update can help the IRLS minimization to recover the sparse signal with lower normalized root mean square error. © 2021 IEEE.