Genetic relaxed iterative Fourier transform algorithm for image reconstruction from Fourier transform magnitude

This paper proposes an algorithm for image reconstruction from the Fourier transform magnitude by means of a genetic algorithm. Since the iterative Fourier transform algorithm involves repetitive application of constraints in the image domain and Fourier domain, correct image reconstruction is not necessarily achieved, and incorrect images may be obtained at certain initial settings (stagnation phenomenon). This study offers a solution to this stagnation problem, specifically, the genetic relaxed iterative Fourier transform algorithm. In it, genetic operations (selection, crossover, and mutation) are employed to avoid stagnation. Computer simulations show that the proposed algorithm is free of stagnation: that is, correct image reconstruction is obtained irrespective of the initial settings. In addition, the proposed algorithm proves faster than the conventional iterative Fourier transform algorithm, and the initial settings are easy to choose because the parameters do not depend on the image features. In this study, binary images are considered. © 2001 Scripta Technica, Syst Comp Jpn, 32(5): 55–63, 2001