  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.
