PHASE RETRIEVAL ALGORITHM BASED ON MAXIMUM ENTROPY METHOD

摘要

The paper presented deals with phase retrieval problem for image reconstruction from only spectrum magnitude. Only two-dimensional spatially limited non-negative objects, which are characterized by analytical spectra, are considered assuming that the unique solution of phase problem exists. In this paper it is proposed to use nonlinear optimization approach, namely, well-known maximum entropy method (MEM) which has very good extrapolation features and high stability to noise. For solving phase retrieval problem we propose to introduce into the optimized entropy functional additional unknowns related to a real and imaginary parts of an object spectrum and represent the constraints, which are derived from measured spectrum magnitude data, as linear constraints, in order to reduce the optimization problem to the standard MEM. The whole computational algorithm is constructed as a combination of the standard MEM algorithm and additional nonlinear constraint for a real and imaginary parts of the spectrum data which is realized during computational iterations. Images reconstructed by the proposed MEM approach may be, if necessary, further improved by Fienup's iterations. In this case the previous image is used as a starting "point ensuring reliable convergence of Fienup's algorithm to sought for solution. Numerous simulation results demonstrate validity and high efficiency of the approach proposed.