Soft Consistency Reconstruction: A Robust 1-bit Compressive Sensing Algorithm

TL;DR

This paper introduces Soft Consistency Reconstructions (SCRs), a new class of algorithms for 1-bit compressive sensing that enhance noise robustness by redesigning the objective function with soft decision criteria.

Contribution

The paper proposes SCRs with re-designed consistency criteria, significantly improving noise robustness in 1-bit CS recovery compared to existing methods.

Findings

SCRs outperform existing algorithms in noisy environments

SCRs maintain comparable performance in high SNR conditions

Soft decisions improve robustness in low SNR regimes

Abstract

A class of recovering algorithms for 1-bit compressive sensing (CS) named Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS recovery is essentially an optimization problem, we endeavor to improve the characteristics of the objective function under noisy environments. With a family of re-designed consistency criteria, SCRs achieve remarkable counter-noise performance gain over the existing counterparts, thus acquiring the desired robustness in many real-world applications. The benefits of soft decisions are exemplified through structural analysis of the objective function, with intuition described for better understanding. As expected, through comparisons with existing methods in simulations, SCRs demonstrate preferable robustness against noise in low signal-to-noise ratio (SNR) regime, while maintaining comparable performance in high SNR regime.