Adaptive Algorithm for Sparse Signal Recovery

TL;DR

This paper introduces an adaptive algorithm based on ADMM for sparse signal recovery that directly tackles non-convex optimization problems, demonstrating superior performance and efficiency over existing methods.

Contribution

The paper proposes a novel adaptive ADMM algorithm that efficiently solves non-convex sparse recovery problems without simplifying assumptions or relaxations.

Findings

Outperforms existing algorithms in accuracy and speed

Effective on both synthetic and real-world data

Reduces computational costs significantly

Abstract

Spike and slab priors play a key role in inducing sparsity for sparse signal recovery. The use of such priors results in hard non-convex and mixed integer programming problems. Most of the existing algorithms to solve the optimization problems involve either simplifying assumptions, relaxations or high computational expenses. We propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the presented optimization problem. The algorithm is based on the one-to-one mapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternating direction method of multipliers to recover the signal corresponding to the updated support. Experiments on synthetic data and real-world images show that the proposed AADMM algorithm provides superior performance and is computationally cheaper, compared to the recently developed iterative convex refinement (ICR) algorithm.