Phase retrieval of block-sparsity via convex optimization

Abstract

Traditional phase retrieval methods for sparse signals are not able to achieve optimal performance when dealing with special-structured signals such as block-sparse signals. In this paper, we focus on the phase retrieval for block k-sparse signal x∈CN, with uniform block size d. Taking advantage of the block-sparse property, an algorithm, called block compressed phase retrieval via lifting (BCPRL), is proposed. The algorithm is not complicated as it combines the classical convex optimization approach for phase retrieval, with the l2,1-minimization for recovery of block sparsity. The analysis with restricted isometry property (RIP) proves that the sample complexity for successful recovery of our algorithm is about d time less than that of conventional sparsity. Simulation results verify that our method provides desirable performance for both block-sparse and conventional sparse signals.