Reconstruction of photon-limited stellar images by generalized projections using the cross spectrum

A new method for finding tight object-support bounds using the cross correlation information is addressed. These bounds are used by the generalized projections method to reconstruct photon-limited atmosphere-degraded images. The iterative Fourier transform (IFT) algorithm or the generalized projections method using the autocorrelation function only, has not been the preferred method for phase retrieval problems. The reason is that the use of the autocorrelation function only does not usually give tight object support bounds. The tight object bounds constraint is crucial for the uniqueness of phase retrieval by the generalized projections. The authors find that the information contained in the average cross correlation of the image and a truncated sub-image of it gives the required tight object bounds