Computing One-bit Compressive Sensing via Double-Sparsity Constrained Optimization
Abstract
One-bit compressive sensing gains its popularity in signal processing and communications due to its low storage costs and low hardware complexity. However, it has been a challenging task to recover the signal only by exploiting the one-bit (the sign) information. In this paper, we appropriately formulate the one-bit compressive sensing into a double-sparsity constrained optimization problem. The first-order optimality conditions for this nonconvex and discontinuous problem are established via the newly introduced -stationarity, based on which, a gradient projection subspace pursuit (\texttt{GPSP}) algorithm is developed. It is proven that \texttt{GPSP} can converge globally and terminate within finite steps. Numerical experiments have demonstrated its excellent performance in terms of a high order of accuracy with a fast computational speed.
Cite
@article{arxiv.2101.03599,
title = {Computing One-bit Compressive Sensing via Double-Sparsity Constrained Optimization},
author = {Shenglong Zhou and Ziyan Luo and Naihua Xiu and Geoffrey Ye Li},
journal= {arXiv preprint arXiv:2101.03599},
year = {2022}
}