A stable direct algorithm for image retrieval from its noisy Fourier transform phase

Owing to the essentially ill-posed nature of the problem of restoration of finite signals and images from their Fourier transform phases, the error in the phase results in large undesired fluctuations in the solution, obtained both by known iterative and direct approaches. The problem of restoration of images from their noisy Fourier transform phases is addressed in relation to the existing solution methods. A new regularizing algorithm is proposed that significantly improves the estimate of an image restored from its noisy phase.