Point-spread function identification in an image restoration problem (Q1380270)

One of the basic classes of reconstruction (restoration) of images, distorted as a result of natural interference action (clouds, atmospheric turbulence), the movement of an object and registering device, and perfectness of the optical and mechanical properties of this device are problems with space-invariant linear distortions of the form \[ Z(x,y)= \iint H(x-\xi, y-\eta)Y(\xi,\eta) d\xi d\eta+ N(x,y),\tag{1} \] where \(Z(x, y)\) is the observed distorted image, \(Y(x, y)\) is the initial image to be reconstructed, \(N(x, y)\) is random noise, and \(H(x, y)\) is the so-called point-spread function (PSF). In some cases, the PSF can be determined a priori by analysis of the physical nature of the problem, but in the majority of real situations it presents some difficulties. The present paper deals with some methods for determining the PSF from a priori and a posteriori information on some part of the observed image with optimal accuracy (with minimal error), because the efficiency of image restoration algorithms depends considerably, and even decisively, on the accuracy of PSF determination.