Compressive Measurement Designs for Estimating Structured Signals in Structured Clutter: A Bayesian Experimental Design Approach

TL;DR

This paper introduces a Bayesian experimental design approach for compressive sensing that leverages prior knowledge to improve signal estimation in noisy, cluttered environments, outperforming traditional random measurement strategies.

Contribution

It develops a novel Bayesian design method for compressive measurements that incorporates prior information about signals and noise, enhancing estimation accuracy.

Findings

Outperforms traditional random measurement designs.

Effective in noisy, cluttered environments.

Leverages prior statistical knowledge for improved sensing.

Abstract

This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or clutter) as well as post-measurement noise, in the specific setting where some (perhaps limited) prior knowledge on the signal, interference, and noise is available. The specific aim here is to devise a strategy for incorporating this prior information into the design of an appropriate compressive measurement strategy. Here, the prior information is interpreted as statistics of a prior distribution on the relevant quantities, and an approach based on Bayesian Experimental Design is proposed. Experimental results on synthetic data demonstrate that the proposed approach outperforms traditional random compressive measurement designs, which are agnostic to the prior information, as well as several other knowledge-enhanced sensing matrix designs based on more heuristic notions.