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) a state-of-the-art algorithm for 1-bit compressive sampling reconstruction. Unlike the BIHT, our model and algorithm does not require prior knowledge on the sparsity of the signal. This makes our proposed work a promising practical approach for signal acquisition.
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