Redundant Dictionary Construction via Genetic Algorithm

Sparse representation of signals based on redundant dictionary is widely used in array signal processing. In this paper, a redundant dictionary construction method via genetic algorithm (GA) is proposed for array signal processing. The problem is formulated as a dictionary selection problem where the dictionary entries are produced by discretizing the angle space. We apply the orthogonality of the entries to evaluate the dictionary according to the Restricted Isometry Property (RIP). GA is used to discretize the angle space which can make the dictionary more orthogonal. Simulation results show that the proposed method can obtain a better division of angle, improving the orthogonality of dictionary effectively, and is suitable for arbitrary observation space compared with commonly used equal angle division and equal sine division.