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This paper considers the problem of reconstructing sparse or compressiblesignals from one-bit quantized measurements. We study a new method that uses alog-sum penalty function, also referred to as the Gaussian entropy, for sparsesignal recovery. Also, in the proposed method, sigmoid functions are introducedto quantify the consistency between the acquired one-bit quantized data and thereconstructed measurements. A fast iterative algorithm is developed byiteratively minimizing a convex surrogate function that bounds the originalobjective function, which leads to an iterative reweighted process thatalternates between estimating the sparse signal and refining the weights of thesurrogate function. Connections between the proposed algorithm and otherexisting methods are discussed. Numerical results are provided to illustratethe effectiveness of the proposed algorithm.

A Fast Iterative Algorithm for Recovery of Sparse Signals from One-Bit Quantized Measurements