Efficient shift-variant image restoration using deformable filtering (Part II): PSF field estimation

We present a two-step technique for estimating the point spread function (PSF) field from a single star field image affected by shift-variant (SV) blur. The first step estimates the best-fitting PSF for each block of an overlapping block grid. We propose a local image model consisting of a pattern (the PSF) being replicated at arbitrary locations and with arbitrary weights. We follow an efficient alternate marginal optimization approach for estimating (1) the most likely pattern, and (2) the locations where it appears in the block, with sub-pixel accuracy. The second step uses linear dimensionality reduction and nonlinear spatial filtering for estimating the entire PSF field from the grid of local PSF estimates. We simulate SV blur on realistic synthetic star fields to assess the accuracy of the method for this kind of images, for different blurs, star densities, and Poisson counts. The results indicate a moderately low error and very robust behavior against noise and artifacts. We also apply our method to real astronomical images, and demonstrate that the method provides relevant information about the underlying structure of the actual telescope and atmosphere PSF fields. We use a variant of the method proposed in Part I to compensate for the observed blur.