Convex Feasibility Methods for Compressed Sensing

TL;DR

This paper introduces a fast, robust convex feasibility approach for compressed sensing that outperforms existing methods in large-scale, noisy, sparse signal recovery tasks.

Contribution

It transforms the convex optimization problem into a convex feasibility problem and applies subgradient projection methods, enhancing efficiency and robustness for large-scale scenarios.

Findings

Subgradient projection methods are fast and robust for large-scale CS.

The proposed approach outperforms Bayesian CS and gradient projection methods in high-dimensional settings.

The method maintains convergence and efficiency despite increased problem size and sparsity.

Abstract

We present a computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS). CS theory requires solving a convex constrained minimization problem. We propose to transform this optimization problem into a convex feasibility problem (CFP), and solve it using subgradient projection methods, which are iterative, fast, robust and convergent schemes for solving CFPs. As opposed to some of the recently-introduced CS algorithms, such as Bayesian CS and gradient projections for sparse reconstruction, which become inefficient as the problem dimension and sparseness degree increase, the newly-proposed methods exhibit a marked robustness with respect to these factors. This renders the subgradient projection methods highly viable for large-scale compressible scenarios.