  The problem of 1-bit compressive sampling is addressed in this paper. We
introduce an optimization model for reconstruction of sparse signals from 1-bit
measurements. The model targets a solution that has the least l0-norm among all
signals satisfying consistency constraints stemming from the 1-bit
measurements. An algorithm for solving the model is developed. Convergence
analysis of the algorithm is presented. Our approach is to obtain a sequence of
optimization problems by successively approximating the l0-norm and to solve
resulting problems by exploiting the proximity operator. We examine the
performance of our proposed algorithm and compare it with the binary iterative
hard thresholding (BIHT) [10] a state-of-the-art algorithm for 1-bit
compressive sampling reconstruction. Unlike the BIHT, our model and algorithm
does not require a prior knowledge on the sparsity of the signal. This makes
our proposed work a promising practical approach for signal acquisition.
