Computing One-Bit Compressive Sensing via Alternating Proximal Algorithm

It is challenging to recover a real sparse signal using one-bit compressive sensing. Existing methods work well when there is no noise (sign flips) in the measurements or the noise level or a priori information about signal sparsity is known. However, the noise level and a priori information about signal sparsity are not always known in practice. In this paper, we propose a robust model with a non-smooth and non-convex objective function. In this model, the noise factor is considered without knowing the noise level or a priori information about the signal sparsity. We develop an alternating proximal algorithm and prove that the sequence generated from the algorithm converges to a local minimizer of the model. Our algrithm possesses high time efficiency and recovery accuracy. It performs better than other algorithms tested in our experiments when the the noise level and the sparsity of the signal is known.