Iterative Re-weighted Least Squares Algorithms for Non-negative Sparse and Group-sparse Recovery

Abstract

Algorithms for non-negative sparse recovery are either based on modifications of orthogonal matching pursuit or are based on thresholding of non-negative least squares. Both are variants of techniques proposed for sparse recovery. This work is based on the iterative re-weighted least squares (IRLS) approach for sparse recovery. IRLS has been found to be a simple yet versatile approach that can handle both l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> -norm and l <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</inf> -quasi norm (0<p<1). We extend this approach to handle not only sparse recovery but also group-sparse recovery.