On Detection-Directed Estimation Approach for Noisy Compressive Sensing

TL;DR

This paper introduces CS-BSD, a Bayesian support detection algorithm for noisy compressive sensing that outperforms existing methods in robustness and speed, utilizing a detection-directed estimation structure.

Contribution

The paper proposes a novel Bayesian support detection algorithm, CS-BSD, with a detection-directed structure that improves robustness and convergence speed in noisy compressive sensing.

Findings

CS-BSD achieves near-MMSE performance at high SNR.

It converges faster than other belief propagation-based algorithms.

CS-BSD can be implemented in parallel for increased speed.

Abstract

In this paper, we investigate a Bayesian sparse reconstruction algorithm called compressive sensing via Bayesian support detection (CS-BSD). This algorithm is quite robust against measurement noise and achieves the performance of a minimum mean square error (MMSE) estimator that has support knowledge beyond a certain SNR threshold. The key idea behind CS-BSD is that reconstruction takes a detection-directed estimation structure consisting of two parts: support detection and signal value estimation. Belief propagation (BP) and a Bayesian hypothesis test perform support detection, and an MMSE estimator finds the signal values belonging to the support set. CS-BSD converges faster than other BP-based algorithms, and it can be converted to a parallel architecture to become much faster. Numerical results are provided to verify the superiority of CS-BSD compared to recent algorithms.