Phase retrieval algorithm based on maximum entropy method

The paper presented deals with phase retrieval problem for image reconstruction from only the spectrum magnitude. Only two-dimensional spatially limited nonnegative objects, which are characterized by the analytical spectra, are considered assuming that the unique solution of the phase problem exists. It is proposed to use a nonlinear optimization approach, namely, the maximum entropy method (MEM) which has very good extrapolation features and a high noise stability. For solving the phase retrieval problem we introduce into the optimized entropy functional additional unknowns related to the 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 an additional nonlinear constraint for the 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 (1982) iterations. In this case the previous image is used as a starting point ensuring reliable convergence of Fienup´s algorithm. Numerous simulation results demonstrate validity and high efficiency of the approach proposed