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A class of recovering algorithms for 1-bit compressive sensing (CS) namedSoft Consistency Reconstructions (SCRs) are proposed. Recognizing that CSrecovery is essentially an optimization problem, we endeavor to improve thecharacteristics of the objective function under noisy environments. With afamily of re-designed consistency criteria, SCRs achieve remarkablecounter-noise performance gain over the existing counterparts, thus acquiringthe desired robustness in many real-world applications. The benefits of softdecisions are exemplified through structural analysis of the objectivefunction, with intuition described for better understanding. As expected,through comparisons with existing methods in simulations, SCRs demonstratepreferable robustness against noise in low signal-to-noise ratio (SNR) regime,while maintaining comparable performance in high SNR regime.

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