Iteratively re-weighted least squares minimization for sparse recovery

TL;DR

This paper analyzes an IRLS algorithm for sparse recovery, proving its convergence, estimating its local rate, and modifying it for lt-minimization to achieve superlinear convergence rates.

Contribution

The paper provides a convergence analysis of IRLS for l1-minimization and introduces modifications for lt-minimization with superlinear convergence.

Findings

Proves convergence of IRLS for l1-minimization.

Estimates local convergence rates.

Modifies IRLS for lt-minimization with superlinear rates.

Abstract

We analyze an Iteratively Re-weighted Least Squares (IRLS) algorithm for promoting l1-minimization in sparse and compressible vector recovery. We prove its convergence and we estimate its local rate. We show how the algorithm can be modified in order to promote lt-minimization for t<1, and how this modification produces superlinear rates of convergence.