This article first provides a historical and detailed introduction to the image formationmodels for diluted pupils array and their densified versions calledhypertelescopes. We propose in particular an original derivationshowing that densification using a periscopic setting like in Michelson’s 20 −  footinterferometer, or using inverted Galilean telescopes are fully equivalent. After a reviewbased on previous reference studies (Tallon & Tallon-Bosc 1992; Labeyrie 1996; Aime 2008 and Aime et al. 2012), the introductory part ends with a tutorialsection for simulating optical interferometric images produced by cophased arrays. Weillustrate in details how the optical image formation model can be used to simulatehypertelescopes images, including sampling issues and their effects on the observedimages.

In a second part of the article, we address the issue of restoring hypertelescope imagesand present numerical illustrations obtained for classical (constrained MaximumLikelihood) methods. We also provide a detailed survey of more recent deconvolutionmethods based on sparse representations and of their spread in interferometric imagereconstruction.

The last part of the article is dedicated to two original and numerical studies. Thefirst study shows by Monte Carlo simulations that the restoration quality achieved byconstrained ML methods applied to photon limited images obtained from a diluted array on asquare grid, or from a densified array (without spectral aliasing) on a grid, areessentially equivalent. The second study shows that it is possible to recover inhypertelescopes images quasi point sources that are not only far outside the clean field,but also superimposed on the replicas of other objects. This is true at least for theconsidered pupil array and in the limit of vanishing noise.