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LINC-NIRVANA (LN) is the Fizeau interferometer of the Large Binocular Telescope which consists of two 8.4 m mirrors with a center-to-center distance of 14.4 m, hence providing a maximum path of 22.8 m in the direction of the baseline joining the two centers. LN is a true imager since interference occurs in the focal plane and not in the aperture plane as with essentially all the existing interferometers. However, an LN image is characterized by an anisotropic resolution: that of a 22.8 m mirror in the direction of the baseline and that of a 8.4 m mirror in the orthogonal direction. In order to obtain a unique image with a high and isotropic resolution, several images must be detected with different orientations of the baseline and suitably processed. Therefore, the instrument will routinely require the use of image reconstruction methods for providing astronomical images with unprecedented resolution, in principle ten times the resolution of the Hubble Space Telescope. This review concerns the image reconstruction problem for LN and is based essentially on our work. After a description of the main features of the telescope and of the interferometer, it contains a discussion of the problem and of the approximations introduced in its formulation. In short, it is reduced to multiple-image deconvolution with Poisson data. Similarity with the image reconstruction problem in emission tomography is stressed and utilized for introducing suitable iterative reconstruction methods. These methods are extended to regularized versions of the problem. Efficiency is another important issue because the size of LN images is of the order of 4.2 megapixels; therefore, acceleration methods are also discussed. All methods are tested on synthetic images because, even if the instrument is in an advanced stage of realization, it will be presumably operative in 2014. The algorithms of the proposed image reconstruction methods are

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