  This paper considers the problem of reconstructing sparse or compressible
signals from one-bit quantized measurements. We study a new method that uses a
log-sum penalty function, also referred to as the Gaussian entropy, for sparse
signal recovery. Also, in the proposed method, sigmoid functions are introduced
to quantify the consistency between the acquired one-bit quantized data and the
reconstructed measurements. A fast iterative algorithm is developed by
iteratively minimizing a convex surrogate function that bounds the original
objective function, which leads to an iterative reweighted process that
alternates between estimating the sparse signal and refining the weights of the
surrogate function. Connections between the proposed algorithm and other
existing methods are discussed. Numerical results are provided to illustrate
the effectiveness of the proposed algorithm.
