Joint deconvolution and semi and unsupervised component separation, with application to radio-interferometry

With the development of continent-wide radio telescopes, the analysis of multi-frequency radio-interferometric data has become a significant challenge in signal processing and astrophysics. In this respect, component separation methods are an adequate tool as they allow to separate multi-frequency data into elementary physical components. However, standard component separation algorithms are not adapted to radio-interferometric data for several reasons: (i) they are constituted of incomplete measurements in the Fourier domain, also known as the visibility domain, and are potentially further deteriorated by instrumental or non-coplanar effects, and (ii) the sought-after signals can be severely drowned in noise or other emissions. Consequently, accounting for the telescope instrumental response requires developing dedicated algorithms to solve a joint deconvolution and separation problem. Furthermore, the recovery of weak signals calls for the design of accurate approaches that make use of physical models known a priori; this motivates the development of semi-supervised separation methods that integrate machine learning techniques. (author)