Opportunistic sensor activation in the face of data deluge

In this paper, we consider the problem of designing optimal measurement policies for a sensor that acquires sequential compressive measurements of a static vector of unknown sparsity as originally formulated in [3]. The scenario is modeled as a finite horizon sequential decision making problem when the number of samples is strictly restricted to be less than the overall horizon of the problem. We assume that at each instant of time 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. We provide a closed-loop optimal measurement policy for a low-dimensional problem. We generalize the optimal policy to obtain a feasible policy for acquiring arbitrary length sparse vectors of unknown sparsity. Finally, we illustrate the performance of the proposed policy by providing simulation results.