HISTORY: An Efficient and Robust Algorithm for Noisy 1-bit Compressed Sensing

TL;DR

HISTORY is a new algorithm designed for robust sparse signal recovery from noisy 1-bit measurements, combining Hamming support detection and coefficients recovery to achieve high accuracy despite severe noise.

Contribution

The paper introduces the HISTORY algorithm, a novel method that improves robustness and accuracy in 1-bit compressed sensing under noisy conditions.

Findings

High recovery accuracy demonstrated

Robustness to strong measurement noise

Outperforms existing methods in simulations

Abstract

We consider the problem of sparse signal recovery from 1-bit measurements. Due to the noise present in the acquisition and transmission process, some quantized bits may be flipped to their opposite states. These sign flips may result in severe performance degradation. In this study, a novel algorithm, termed HISTORY, is proposed. It consists of Hamming support detection and coefficients recovery. The HISTORY algorithm has high recovery accuracy and is robust to strong measurement noise. Numerical results are provided to demonstrate the effectiveness and superiority of the proposed algorithm.