Phase retrieval based on an Evolutionary Multicriterion Optimisation method

Phase problems arise from lost phase information in measurement of diffraction waves. The missing phase should be retrieved to reconstruct an object image from the diffraction pattern. This paper proposes a hybrid type approach, Evolutionary-based GS (E-GS), based on the Gerchberg - Saxton algorithm (GS algorithm) and Evolutionary Multicriterion Optimisation (EMO). There are three main aims of E-GS: (1) to reduce the dependence on initial conditions, (2) to obtain some candidate solutions with various features in one trial and (3) to achieve algorithmic parallelism. In E-GS, the phase retrieval problem is formulated as a two-objective optimisation problem, and the EMO and GS algorithm are used as the framework of multiobjective optimisation and local search, respectively. E-GS deals directly with phase as an optimisation parameter and embeds original genetic operations based on frequency characteristics. In this paper, the characteristics and effectiveness of the proposed approach are discussed by comparison of the performance with that of the GS algorithm. Through numerical examples, it was demonstrated that E-GS could derive good results and the difference of search transition between GS algorithm and E-GS was clarified.