Solving a problem of sources separation stemming from a linear combination: Applied to the 3D reconstruction of the solar atmosphere

In this article, we propose to reconstruct the 3D structure of the solar atmosphere, taking into account the temporal evolution of the coronal structures. To do this we develop a new method, which considers that the object of interest consists of several sources each one having different evolution from the other at different time. The data are the Radon transform of an instantaneous mixture of sources. So, we must solve a separation source problem with a linear mixture of sources. To our best knowledge, this problem is still open. To solve this problem of source separation, we have introduced a sparsity information on the sources, and we have chosen to use the variational Bayesian approach for reduce the computation time.