  One-bit compressed sensing is very popular in signal processing and
communications due to its low storage costs and low hardware complexity, but it
is a challenging task to recover the signal by using the one-bit information.
In this paper, we propose a zero-norm regularized smooth difference of
convexity (DC) loss model and derive a family of equivalent nonconvex
surrogates covering the MCP and SCAD surrogates as special cases. Compared to
the existing models, the new model and its SCAD surrogate have better
robustness. To compute their $\tau$-stationary points, we develop a proximal
gradient algorithm with extrapolation and establish the convergence of the
whole iterate sequence. Also, the convergence is proved to have a linear rate
under 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 of
the quality of solution, the proposed model and its SCAD surrogate are
remarkably superior to the $\ell_p$-norm regularized models, and are comparable
even superior to those sparsity constrained models with the true sparsity and
the sign flip ratio as inputs.
