IMAGE-RECONSTRUCTION FROM FOURIER-TRANSFORM MAGNITUDE WITH APPLICATIONS TO SYNTHETIC-APERTURE RADAR IMAGING

The problem of reconstructing an unknown signal starting from the know ledge of only magnitude information about its Fourier transform is add ressed. To this end a phase retrieval (PR) method, based on the invers ion of a quadratic operator, is proposed, presented, and discussed. Th e main feature of the approach is the use of a square amplitude distri bution rather than an amplitude distribution. In the lack of any a pri ori information about the phase to be recovered, the success of the me thod is related to the availability of a sufficiently large ratio betw een the dimension of data and the dimension of unknowns; the retrieval procedure could converge to a meaningless trap when this ratio is not large enough. It should be noted, however, that the proposed method h as a range of global effectiveness wider than that of previous approac hes. Moreover, when available, the use of a priori information, such a s the knowledge of the support of the scene to be imaged or the knowle dge of a part of the scene, allows one to achieve accurate final image s starting from a completely random initial guess of the image values. We apply our PR-based method to a synthetic aperture radar (SAR) case . As is well known, random motion of the platform and/or propagation e ffects in turbulent random media can affect the correct phase synchron ization of the received SAR raw data needed for well-focused SAR image s. As a matter of fact, even relatively small phase errors greatly imp air the quality of the image. Under common conditions phase errors on the received signal affect just the phase of the Fourier transform of the intensity image without impairing its amplitude. The proposed tech nique is able to compensate these phase errors by retrieving the phase of the Fourier transform of the image intensity. We also present seve ral experiments performed either on numerically simulated data or on a ctual data relative to an airborne SAR mission that show the effective ness of the proposed PR method. (C) 1996 Optical Society of America