Multipath Matching Pursuit

TL;DR

This paper introduces the multipath matching pursuit algorithm, a greedy tree search method for sparse signal recovery from compressed measurements, demonstrating effectiveness in noiseless and noisy conditions with theoretical guarantees.

Contribution

The paper presents a novel multipath matching pursuit algorithm that explores multiple candidates simultaneously, improving sparse signal reconstruction over existing methods.

Findings

Effective in noiseless and noisy scenarios

Provides RIP-based performance guarantees

Outperforms some existing sparse recovery algorithms

Abstract

In this paper, we propose an algorithm referred to as multipath matching pursuit that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to find the candidate that minimizes the residual is readily modeled as a combinatoric tree search problem and the greedy search strategy is a good fit for solving this problem. In the empirical results as well as the restricted isometry property (RIP) based performance guarantee, we show that the proposed MMP algorithm is effective in reconstructing original sparse signals for both noiseless and noisy scenarios.