Deconvolved Image Restoration From Auto-Correlations

Recovering a signal from auto-correlations or, equivalently, retrieving the phase linked to given Fourier modulus, is wide-spread problem in imaging. This has been tackled number of experimental situations, optical microscopy adaptive astronomy, making use assumptions based on constraints and prior information about recovered object. In similar fashion, deconvolution another common imaging, particular within community, allowing high-resolution reconstruction blurred images. Here we address mixed performing auto-correlation inversion while, at same time, deconvolving its current estimation. To this end, propose an I-divergence optimization, driving our formalism into widely used iterative scheme, inspired by Bayesian-based approaches. We demonstrate method recovering auto-correlations, further analysing cases objects band-limited measurements.