Reconstruction of an object from its noisy Fourier modulus: ideal estimateof the object to be reconstructed and a method that attempts to find that estimate

In general, the problem of reconstructing an object hom its Fourier modulus has no solution when the Fourier modulus is contaminated by noise. Therefo re a quasi solution, which we call the ideal estimate of the object to be r econstructed, is defined here based on the concept of territories of the co nvergence objects of the error-reduction algorithm, and a method that attem pts to find that solution is presented. Keeping in mind that the ideal esti mate is one of the output-stagnation objects of the hybrid input-output alg orithm, we modify the hybrid input-output algorithm so that the output-stag nation objects can be located even when the value of the feedback parameter is not infinitesimally small, and this modified algorithm is combined with the hybrid input-output algorithm itself. The results of computer simulati ons carried out to test the performance of the proposed method are shown. ( C) 1999 Optical Society of America.