Restoration of interferometric images - III. Efficient Richardson-Lucy methods for LINC-NIRVANA data reduction

In previous papers we proposed methods and software for the restoration of images provided by Fizeau interferometers such as LINC-NIRVANA (LN), the German-Italian beam combiner for the Large Binocular Telescope (LBT). It will provide multiple images of the same target corresponding to different orientations of the baseline. Therefore LN will require routinely the use of multiple-image deconvolution methods in order to produce a unique high-resolution image. As a consequence of the complexity of astronomical images, two kinds of methods will be required: first a quick-look method, namely a method that is computationally efficient, allowing a rapid overview and identification of the object being observed; second an ad hoc method designed for that particular object and as accurate as possible. In this paper we investigate the possibility of using Richardson-Lucy-like (RL-like) methods, namely methods designed for the maximization of the likelihood function in the case of Poisson noise, as possible quick-look methods. To this purpose we propose new techniques for accelerating the Ordered Subsets-Expectation Maximization (OS-EM) method, investigated in our previous papers; moreover, we analyze approaches based on the fusion of the multiple images into a single one, so that one can use single-image deconvolution methods which are presumably more efficient than the multiple-image ones. The results are encouraging and all the methods proposed in this paper have been implemented in our software package AIRY.