Adaptive matching pursuit for sparse signal recovery

TL;DR

This paper introduces an adaptive matching pursuit algorithm that efficiently solves the non-convex sparse recovery problem with Spike and Slab priors, improving speed and accuracy in signal processing tasks.

Contribution

A novel greedy adaptive matching pursuit algorithm that directly tackles the non-convex sparse recovery problem with improved computational efficiency.

Findings

Outperforms existing methods in simulated data recovery tasks.

Provides a better cost-quality trade-off in real-world image recovery.

Uses inexpensive Cholesky decomposition for faster intermediate computations.

Abstract

Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and classification. It is well-known that solving for the sparse coefficient vector to maximize these priors results in a hard non-convex and mixed integer programming problem. Most existing solutions to this optimization problem either involve simplifying assumptions/relaxations or are computationally expensive. We propose a new greedy and adaptive matching pursuit (AMP) algorithm to directly solve this hard problem. Essentially, in each step of the algorithm, the set of active elements would be updated by either adding or removing one index, whichever results in better improvement. In addition, the intermediate steps of the algorithm are calculated via an inexpensive Cholesky decomposition which makes the algorithm much faster. Results on simulated data sets as well as real-world image recovery challenges confirm the benefits of the proposed AMP, particularly in providing a superior cost-quality trade-off over existing alternatives.