Regularization of the problem of image restoration from its noisy Fourier transform phase

Abstract

In all papers published earlier the phase of the Fourier transform of an image was assumed to be known exactly. This assumption, however, is not valid in practice, since the image phase can be measured or processed only with some error. Owing to the essentially ill-posed nature of the restoration problem this error results in substantial undesired fluctuations in the solution, obtained both by known iterative and direct approaches. In this paper, the problem of restoration of images from their Fourier transform phases is considered as the ill-posed one that calls for using the corresponding regularization algorithms. The regularization algorithm is proposed that significantly improves an estimate of an image restored from the noisy phase.