Joint deconvolution and unsupervised source separation for data on the sphere

Abstract

Tackling unsupervised source separation jointly with an additional inverse problem such as deconvolution is central for the analysis of multi-wavelength data. This becomes highly challenging when applied to large data sampled on the sphere such as those provided by wide-field observations in astrophysics, whose analysis requires the design of dedicated robust and yet effective algorithms. We therefore investigate a new joint deconvolution/sparse blind source separation method dedicated for data sampled on the sphere, coined SDecGMCA. It is based on a projected alternate least-squares minimization scheme, whose accuracy is proved to strongly rely on some regularization scheme in the present joint deconvolution/blind source separation setting. To this end, a regularization strategy is introduced that allows designing a new robust and effective algorithm, which is key to analyze large spherical data. Numerical experiments are carried out on toy examples and realistic astronomical data.