Adaptive compressive sensing in the presence of noise and erasure

We consider an application of adaptive compressive sensing for estimating time-varying sparse signals. The scenario entails the corruption of the sparse signal by additive observational noise and erasure. We formulate the problem as a partially observable Markov decision process (POMDP) and apply a multi-step lookahead solution technique, rollout. To reduce computations involved in the posterior distribution propagation and improve estimates of the unobservable state, we incorporate an approximation adapted from multiple hypothesis tracking. Each action decision selects a fixed size measurement matrix from a predefined library composed of matrices whose rows are members of a Grassmannian packing. The performance of the matrix selections is gauged by the ability to maximize the conditional mutual information between the sparse signal support and the resulting observations. Through simulation, we compare rollout with an adaptive heuristic and a greedy algorithm.