Soft Consistency Reconstruction: A robust 1-bit compressive sensing algorithm

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.