One-bit compressive sensing and source localization in wireless sensor networks

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. Additionally, in the proposed method, the sigmoid function is introduced to quantify the consistency between the measured one-bit quantized data and the reconstructed signal. A fast iterative algorithm is developed by iteratively minimizing a convex surrogate function that bounds the original objective function. This leads to an iterative reweighted process that alternates between estimating the sparse signal and refining the weights of the surrogate function. The application of one-bit compressed sensing to source localization in wireless sensor networks is also discussed. Simulations are provided to illustrate the effectiveness of our proposed algorithm.