Astronomical image deconvolution using sparse priors: An analysis-by-synthesis approach

This paper deals with the deconvolution of faint diffuse astronomical sources buried in the PSF sidelobes of surrounding bright compact sources, and in the noise. We propose a sparsity promoting restoration model which is based on highly redundant, shift invariant dictionaries, and which is hybrid in its sparsity priors. On one hand, the image to be restored is modelled using sparse synthesis priors as a sum of few atoms (objects) which, as opposed to classical synthesis-based priors, are unknown. On the other hand, these objects are iteratively estimated and deconvolved through analysis-based priors. The faint diffuse source is deconvolved once the data has been cleaned from all brighter sources´ contributions. Comparative numerical results show that the method is efficient and fast.