  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.
