Image reconstruction with variable resolution using Gaussian Invariant functions in a segmentation process

Abstract In this paper we present a method of image reconstruction that uses a Maximum a Posteriori Bayesian algorithm with Entropy prior (FMAPE), with hyperparameters that are region dependent. The space variant hyperparameter determines the relative weight between the prior information and the likelihood, defining the degree of smoothness of the solution in each region. This method responds to the premise that the resolution sought in the reconstruction of different parts of an image should depend on the statistical quality of the corresponding data. A two-step segmentation process using Gaussian Invariant functions is applied to a Maximum Likelihood reconstruction. In the first step all the stars are separated from the image field. In the second, the rest of the image is segmented into a number of sections with similar statistical quality. We then carry out the FMAPE reconstruction with hyperparameters adjusted automatically so that the residuals have an approximately correct variance in each of the segmented regions. The method has been applied to data from the non-refurbished Hubble Space Telescope. Results show very low bias and high image quality.