A Fast Iterative Algorithm for Recovery of Sparse Signals from One-Bit Quantized Measurements

TL;DR

This paper introduces a fast iterative algorithm for reconstructing sparse signals from one-bit quantized measurements, utilizing a log-sum penalty and sigmoid functions to improve accuracy and efficiency.

Contribution

The paper proposes a novel iterative reweighted algorithm based on a log-sum penalty for one-bit compressed sensing, enhancing recovery performance.

Findings

Effective in reconstructing sparse signals from one-bit data

Outperforms existing methods in accuracy and speed

Numerical results validate the proposed algorithm's efficiency

Abstract

This paper considers the problem of reconstructing sparse or compressible signals from one-bit quantized measurements. We study a new method that uses a log-sum penalty function, also referred to as the Gaussian entropy, for sparse signal recovery. Also, in the proposed method, sigmoid functions are introduced to quantify the consistency between the acquired one-bit quantized data and the reconstructed measurements. A fast iterative algorithm is developed by iteratively minimizing a convex surrogate function that bounds the original objective function, which leads to an iterative reweighted process that alternates between estimating the sparse signal and refining the weights of the surrogate function. Connections between the proposed algorithm and other existing methods are discussed. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.