Bio-electric current density imaging via an iterative algorithm with joint sparsity constraints

Neuronal current imaging aims at analyzing the functionality of the human brain through the localization of those regions where the neural current flows. The reconstruction of an electric current distribution from its magnetic field measured by sophisticated superconducting devices in a noninvasive way, gives rise to a highly ill-posed and ill-conditioned inverse problem. Assuming that each component of the current density vector possesses the same sparse representation with respect to a preassigned multiscale basis, allows us to apply new regularization techniques to the magnetic inverse problem. In particular, we use a joint sparsity constraint as a regulariza- tion term and we propose an efficient iterative thresholding algorithm to reconstruct the current distribution. Some bidimensional experiments are presented in order to show the algorithm properties.