We consider the estimation of the Brain Electrical Sources (BES) matrix from noisy electroencephalographic (EEG)\nmeasurements, commonly named as the EEG inverse problem. We propose a new method to induce\nneurophysiological meaningful solutions, which takes into account the smoothness, structured sparsity, and low rank\nof the BES matrix. The method is based on the factorization of the BES matrix as a product of a sparse coding matrix\nand a dense latent source matrix. The structured sparse-low-rank structure is enforced by minimizing a regularized\nfunctional that includes the 21-norm of the coding matrix and the squared Frobenius norm of the latent source\nmatrix. We develop an alternating optimization algorithm to solve the resulting nonsmooth-nonconvex minimization\nproblem. We analyze the convergence of the optimization procedure, and we compare, under different synthetic\nscenarios, the performance of our method with respect to the Group Lasso and Trace Norm regularizers when they\nare applied directly to the target matrix.
Loading....