Compressive Measurement Designs for Estimating Structured Signals in Structured Clutter: A Bayesian Experimental Design Approach
This work addresses estimation in compressive sensing with prior information, offering a method for improved measurement design, but it is incremental as it builds on existing Bayesian and compressive sensing frameworks.
The paper tackles the problem of estimating structured signals in compressive sensing with prior knowledge on signal, interference, and noise, proposing a Bayesian Experimental Design approach to design compressive measurements, and experimental results show it outperforms random and heuristic designs.
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.