A Hybrid Particle Swarm Optimization-Based Algorithm for 1-D Phase Retrieval

The previous solutions for 1-D phase retrieval problem usually employed an iterative algorithm applied on a discrete approximation of a signal. The utilization of these algorithms is seriously limited by the unpredictability of their convergence, stagnation and abundant computation. In this paper, a particle swarm optimization algorithm is introduced to solve this problem. Firstly, 1-D phase retrieval was regarded as a constrained nonlinear optimization problem. Secondly, it was converted to an unconstrained nonlinear optimization problem by using penalty function method. Finally, a particle swarm optimization algorithm incorporated with hill-climbing method was used to solve this optimization problem. The effectiveness of our solution is illustrated with some numerical examples.