Phase retrieval from photon-limited data using the cross correlation

An image reconstruction algorithm from a series of short exposure images using the average cross-correlation between observation and a truncated part of it is described. The idea behind this method is that the edges of the stars contained in the part of the unknown object corresponding to the brightest regions in the observed images are preserved in the cross correlation. The information about these edges is then used to recover the phase of the whole object. Results from computer-simulated data and from real data show that the phase estimation errors of the present cross-spectrum method are smaller than those of the triple-correlation bispectrum method