On the reconstruction of an object image from the modulus of fourier - Transform

The convergence of an iterative procedure, proposed earlier for the reconstruction of a finite-size object image from the modulus of its Fourier-transform, was investigated by means of a computer experiment. The investigation results confirmed the good convergence of the process to the correct result from some its neighborhood in the image space was confirmed, as well as, the probability of convergence to an incorrect result (called 'trap'), in the case of a random initial approximation. A discrete nature of a trap set was established. Fractal-like dependence of the process convergence limit on the initial approximation was found. A probability of the correct image reconstruction with a random initial approximation was estimated. The results obtained are illustrated with graphics, half-tone images and color maps. © 2009 Begell House, Inc.