Montoya-Martinez, Jair6; Artes-Rodriguez, Antonio6; Pontil, Massimiliano4; Hansen, Lars Kai5
1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Cognitive Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Universidad Carlos III de Madrid4 University College London5 Copenhagen Center for Health Technology, Center, Technical University of Denmark6 Universidad Carlos III de Madrid
We consider the estimation of the Brain Electrical Sources (BES) matrix from noisy electroencephalographic (EEG) measurements, commonly named as the EEG inverse problem. We propose a new method to induce neurophysiological meaningful solutions, which takes into account the smoothness, structured sparsity, and low rank of the BES matrix. The method is based on the factorization of the BES matrix as a product of a sparse coding matrix and a dense latent source matrix. The structured sparse-low-rank structure is enforced by minimizing a regularized functional that includes the ℓ21-norm of the coding matrix and the squared Frobenius norm of the latent source matrix. We develop an alternating optimization algorithm to solve the resulting nonsmooth-nonconvex minimization problem. We analyze the convergence of the optimization procedure, and we compare, under different synthetic scenarios, the performance of our method with respect to the Group Lasso and Trace Norm regularizers when they are applied directly to the target matrix.
Eurasip Journal on Advances in Signal Processing, 2014, Vol 2014, Issue 97