Digital signal processing solutions to 2-D phase retrieval problems

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 and alternate between the spatial and wavenumber domains. These algorithms are not POCS and they tend to stagnate. We present a completely novel approach that uses a battery of digital signal processing algorithms to produce an algorithm that comes close to expressing the solution in closed form. The only requirement on the image is that it have finite spatial extent and be roughly bandlimited so that a fractional spatial shift also has finite spatial extent (this requirement is almost always met in practice)