In this paper we give a survey of the methods we have developed for
multiple image deconvolution, with application to the reconstruction of
the images of the Large Binocular Telescope (LBT). We first describe
the main features of LBT and of the Fizeau interferometer, denoted
LINC-NIRVANA, that will be one of the basic instruments of the telescope.
It will allow to reach the resolution of a 22.8 m mirror by combining
different images taken with different orientations of the baseline. Next
we discuss the problem of multiple image deconvolution, that is crucial for
obtaining a unique high-resolution image from the multiple images provided
by LINC-NIRVANA. We present the state-of-the art of the methods based on
the Richardson-Lucy (RL) approach and we discuss topics such as
computational efficiency, correction of boundary effects and super-resolution.
Then, in the perspective of going beyond RL, we extend to the problem of
multiple image deconvolution the split gradient method (SGM) that is
a general approach to the design of iterative methods for the constrained
minimization of regularized functionals. Finally we present an application
of SGM to the regularized reconstruction of objects with high-dynamic range.
The different methods are illustrated with examples taken from the many
numerical experiments we performed on this problem.