Optimized selection of random expander graphs for Compressive Sensing

Compressive Sensing (CS) shows that sparse signals can be exactly recovered from a limited number of random or deterministic projections when the measurement mode satisfies some specified conditions. Random matrices, with the drawbacks of large storage, low efficiency and high complexity, are hard to use in practical applications. Recent works explore expander graphs for efficient CS recovery, but there is no explicit construction of expanders. The widely used expanders are chosen at random based on the probabilistic method. In this paper, we propose a parameter based on the second-largest eigenvalue of the adjacency matrix to select optimized expanders from random expanders. The theoretical analysis and the numerical simulations both indicate the selection criteria proposed in this paper can pick up the high-performance expanders from the random expanders effectively.