Phase retrieval of images from zeros of even unwrapped signals

The 2-D discrete phase retrieval problem is to reconstruct an image defined at integer coordinates and having known finite spatial extent from the magnitude of its discrete Fourier transform. Most methods for solving this problem are iterative but not POCS, and they tend to stagnate. Recently we developed a new approach that unwrapped the 2-D problem into a 1-D problem with bands of zeros in it, using the Good-Thomas FFT. However, this approach reconstructed the even part of the image much better than the odd part, and it was sensitive to the zero locations. This paper presents a modification of this approach. New features include: (1) an overdetermined problem less sensitive to the zero locations; (2) the solution of a Toeplitz-block-Toeplitz-plus-Hankelblock-Hankel linear system; and (3) details on characteristics of images for which the approach works best.