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One-bit compressed sensing is very popular in signal processing andcommunications due to its low storage costs and low hardware complexity, but itis a challenging task to recover the signal by using the one-bit information.In this paper, we propose a zero-norm regularized smooth difference ofconvexity (DC) loss model and derive a family of equivalent nonconvexsurrogates covering the MCP and SCAD surrogates as special cases. Compared tothe existing models, the new model and its SCAD surrogate have betterrobustness. To compute their $\tau$-stationary points, we develop a proximalgradient algorithm with extrapolation and establish the convergence of thewhole iterate sequence. Also, the convergence is proved to have a linear rateunder a mild condition by studying the KL property of exponent 0 of the models.Numerical comparisons with several state-of-art methods show that in terms ofthe quality of solution, the proposed model and its SCAD surrogate areremarkably superior to the $\ell_p$-norm regularized models, and are comparableeven superior to those sparsity constrained models with the true sparsity andthe sign flip ratio as inputs.

Computing one-bit compressive sensing via zero-norm regularized DC loss model and its surrogate