Computing One-bit Compressive Sensing via Double-Sparsity Constrained Optimization

TL;DR

This paper introduces a novel optimization framework for one-bit compressive sensing, formulating it as a double-sparsity constrained problem and proposing an efficient algorithm with proven convergence.

Contribution

It develops a new nonconvex optimization model for one-bit sensing and introduces the GPSP algorithm with global convergence guarantees.

Findings

GPSP converges globally and terminates in finite steps.

Numerical experiments show high accuracy and fast computation.

The method outperforms existing approaches in efficiency and accuracy.

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 $\tau$-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.