Design of Optimal Measurement Matrix for Compressive Detection

This paper considers the problem of designing measurement matrix Phi for compressive detection. Since the objective of detection is to extract certain information from measurements rather than to reconstruct the sparse signals, the optimal measurement matrix design is formulated in terms of maximizing the detection probability. Based on the relationship between Phi and the detection probability, it is revealed that the solutions are only related to the right singular vectors of Phi. The optimal Phi are obtained for a given sparse signal pattern. For the situation when the sparse signal patterns are unknown, the optimal measurement design problem is defined as maximizing the worst-case detection probability. An algorithm is derived to solve the corresponding problem. Simulation results show that the measurement matrix obtained using the proposed algorithm outperforms the popularly used random matrix in terms of detection probability.