  Blind Source Separation (BSS) is a challenging matrix factorization problem
that plays a central role in multichannel imaging science. In a large number of
applications, such as astrophysics, current unmixing methods are limited since
real-world mixtures are generally affected by extra instrumental effects like
blurring. Therefore, BSS has to be solved jointly with a deconvolution problem,
which requires tackling a new inverse problem: deconvolution BSS (DBSS). In
this article, we introduce an innovative DBSS approach, called DecGMCA, based
on sparse signal modeling and an efficient alternative projected least square
algorithm. Numerical results demonstrate that the DecGMCA algorithm performs
very well on simulations. It further highlights the importance of jointly
solving BSS and deconvolution instead of considering these two problems
independently. Furthermore, the performance of the proposed DecGMCA algorithm
is demonstrated on simulated radio-interferometric data.
