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(arXiv abridged abstract) The current years are seeing huge developments ofradio telescopes and a tremendous increase of their capabilities. Such systemsmake mandatory the design of more sophisticated techniques not only fortransporting, storing and processing this new generation of radiointerferometric data, but also for restoring the astrophysical informationcontained in such data. In this paper we present a new radio deconvolutionalgorithm named MORESANE and its application to fully realistic simulated dataof MeerKAT, one of the SKA precursors. This method has been designed for thedifficult case of restoring diffuse astronomical sources which are faint inbrightness, complex in morphology and possibly buried in the dirty beam's sidelobes of bright radio sources in the field. MORESANE is a greedy algorithmwhich combines complementary types of sparse recovery methods in order toreconstruct the most appropriate sky model from observed radio visibilities. Asynthesis approach is used for the reconstruction of images, in which thesynthesis atoms representing the unknown sources are learned using analysispriors. We apply this new deconvolution method to fully realistic simulationsof radio observations of a galaxy cluster and of an HII region in M31. We showthat MORESANE is able to efficiently reconstruct images composed from a widevariety of sources from radio interferometric data. Comparisons with otheravailable algorithms, which include multi-scale CLEAN and the recently proposedmethods by Li et al. (2011) and Carrillo et al. (2012), indicate that MORESANEprovides competitive results in terms of both total flux/surface brightnessconservation and fidelity of the reconstructed model. MORESANE seemsparticularly well suited for the recovery of diffuse and extended sources, aswell as bright and compact radio sources known to be hosted in galaxy clusters.

MORESANE: MOdel REconstruction by Synthesis-ANalysis Estimators. A sparse deconvolution algorithm for radio interferometric imaging