Adaptive compressive sampling using partially observable markov decision processes

We present an approach to adaptive measurement selection in compressive sensing for estimating sparse signals. Given a fixed number of measurements, we consider the sequential selection of the rows of a compressive measurement matrix to maximize the mutual information between the measurements and the sparse signal's support. We formulate this problem as a partially observable Markov decision process (POMDP), which enables the application of principled reasoning for sequential measurement selection based on Bellman's optimality condition.