Optimal acquisition policy for compressed measurements with limited observations

In this paper, we explore the problem of optimizing the measurement policy in finite horizon sequential compressive sensing when the number of samples are strictly restricted to be less than the overall horizon of the problem. We assume that at each instant the sensor can decide whether or not to take an observation, based on the quality of the sensing parameters. The objective of the sensor is to minimize the coherence of the final sensing matrix. This problem lies at the intersection of usage limited sensing [6], [11] and sequential compressive sensing [3]. First, we consider the optimal acquisition problem in the class of open-loop policies. We show that every open-loop policy that satisfies the sensing constraints is optimal. Next, we consider the set of closed-loop policies. In order to solve the optimal acquisition problem, we formulate the corresponding dynamic program. Finally, we propose a greedy strategy for acquiring measurements, and show that it is optimal for low-dimensional problems.