CONVERGENCE OF ITERATIVE PHASE RETRIEVAL IMPROVED BY UTILIZING ZERO SHEETS

It is now known that a complex-valued image may be recovered from the modulus of its Fourier transform using a support constraint. Convergence of the iterative algorithms used for this purpose, however, can be slow. A new zero matching technique, based on the concept of the zero sheet (of the spectrum of a compact image), that can be incorporated into existing iterative algorithms, is described. In contrast to previous methods using zero sheets, the new method is applicable to contaminated Fourier data. Reconstruction results for complex and positive images show the methods's ability to significantly improve the convergence of iterative algorithms. In some cases, stagnation is overcome by applying the new technique. Best results to date have been obtained by a combination of Fienup's hybrid input-output and error reduction algorithms with the new zero matching technique.