We define self-cross correlation as the cross correlation between an image and a truncated part of it. A new method for finding tight object-support bounds by use of the self-cross-correlation information is addressed. These bounds are used in the generalized-projection method to reconstruct photon-limited atmosphere-degraded images. The iterative Fourier-transform algorithm and the generalized-projection method, with use of the autocorrelation function only, have not been preferred to the Knox–Thompson and the triple-correlation methods for phase-retrieval problems, because the use of the autocorrelation function only usually does not give tight object-support bounds. The tight-object-support-bounds constraint is crucial for the uniqueness of phase retrieval by generalized projections. We find that the information contained in the average self cross correlation gives the required tight object-support bounds. The advantage of our method over the triple-correlation method lies in the speed of computation.
© 1994 Optical Society of America
Original Manuscript: December 30, 1991
Revised Manuscript: September 7, 1993
Manuscript Accepted: November 9, 1993
Published: May 1, 1994
Xiaotian Shi and Rabab K. Ward, "Reconstruction of photon-limited stellar images by generalized projections with use of the self-cross spectrum," J. Opt. Soc. Am. A 11, 1589-1598 (1994)