Robust 1-bit Compressive Sensing via Gradient Support Pursuit

TL;DR

This paper introduces a robust method for 1-bit compressed sensing using a modified Gradient Support Pursuit algorithm, demonstrating improved noise robustness and efficiency in low to mid SNR regimes.

Contribution

It applies a modified Gradient Support Pursuit algorithm to 1-bit compressed sensing, showing theoretical accuracy and superior performance over existing methods.

Findings

Accurately solves 1-bit CS with stable restricted Hessian assumption

Outperforms state-of-the-art algorithms in noisy environments

Achieves better reconstruction SNR vs. time trade-off at low to mid SNRs

Abstract

This paper studies a formulation of 1-bit Compressed Sensing (CS) problem based on the maximum likelihood estimation framework. In order to solve the problem we apply the recently proposed Gradient Support Pursuit algorithm, with a minor modification. Assuming the proposed objective function has a Stable Restricted Hessian, the algorithm is shown to accurately solve the 1-bit CS problem. Furthermore, the algorithm is compared to the state-of-the-art 1-bit CS algorithms through numerical simulations. The results suggest that the proposed method is robust to noise and at mid to low input SNR regime it achieves the best reconstruction SNR vs. execution time trade-off.