Inverse filtering by signal reconstruction from phase

Abstract

A common problem that arises in image processing is that of performing inverse filtering on an image that has been blurred. Methods for doing this have been developed, but require fairly accurate knowledge of the magnitude of the Fourier transform of the blurring function and are sensitive to noise in the blurred image. It is known that a typical image is defined completely by its region of support and a sufficient number of samples of the phase of its Fourier transform. We will investigate a new method of deblurring images based only on phase data. It will be shown that this method is much more robust in the presence of noise than existing methods and that, because no magnitude information is required, it is also more robust to an incorrect guess of the blurring filter. Methods of finding the region of support of the image will also be explored.