Sparse signal recovery from one-bit quantized data: An iterative reweighted algorithm

Jun Fang, Yanning Shen, Hongbin Li, Zhi Ren

Abstract: Highlights • A new iterative algorithm for sparse signal recovery from 1-bit quantized data. • Introduced a new sigmoid-function based approach for consistency checking. • Employs a convex surrogate function based bounding technique for optimization. Abstract This paper considers the problem of reconstructing sparse signals from one-bit quantized measurements. We employ a log-sum penalty function, also referred to as the Gaussian entropy, to encourage sparsity in the algorithm development. In addition, in the proposed method, the logistic function is introduced to quantify the consistency between the measured one-bit quantized data and the reconstructed signal. Since the logistic function has the tendency to increase the magnitudes of the solution, an explicit unit-norm constraint is no longer necessary to be included in our optimization formulation. An 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. Numerical results are provided to illustrate the effectiveness of the proposed algorithm.