Matching Pursuit LASSO Part II: Applications and Sparse Recovery over Batch Signals

TL;DR

This paper introduces a batch-mode Matching Pursuit LASSO algorithm that significantly accelerates sparse recovery for multiple signals simultaneously, demonstrating superior speed and accuracy over existing methods in practical applications.

Contribution

It develops a novel batch-mode MPL algorithm with a subspace search to enhance performance and handle large-scale batch sparse recovery tasks efficiently.

Findings

BMPL is up to 400 times faster than state-of-the-art $ ext{l}_1$-norm methods.

The proposed methods outperform existing techniques in sparse recovery accuracy.

Numerical experiments confirm the efficiency and effectiveness of BMPL in practical applications.

Abstract

Matching Pursuit LASSIn Part I \cite{TanPMLPart1}, a Matching Pursuit LASSO ({MPL}) algorithm has been presented for solving large-scale sparse recovery (SR) problems. In this paper, we present a subspace search to further improve the performance of MPL, and then continue to address another major challenge of SR -- batch SR with many signals, a consideration which is absent from most of previous $\ell_1$-norm methods. As a result, a batch-mode {MPL} is developed to vastly speed up sparse recovery of many signals simultaneously. Comprehensive numerical experiments on compressive sensing and face recognition tasks demonstrate the superior performance of MPL and BMPL over other methods considered in this paper, in terms of sparse recovery ability and efficiency. In particular, BMPL is up to 400 times faster than existing $\ell_1$-norm methods considered to be state-of-the-art.O Part II: Applications and Sparse Recovery over Batch Signals