Structured Sparse-Low Rank Matrix Factorization For The EEG Inverse Problem
Jair Montoya-Martínez, Antonio Artés-Rodríguez, Massimiliano Pontil

We consider the estimation of the Brain Electrical Sources (BES) matrix from noisy EEG measurements, commonly named as the EEG inverse problem. We propose a new method based on the factorization of the BES as a product of a sparse coding matrix and a dense latent source matrix. This structure is enforced by minimizing a regularized functional that includes the $\ell_{21}$-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 have evaluated our approach under a simulated scenario consisting on estimating a synthetic BES matrix with 5124 sources. We compare the performance of our method respect to the Lasso, Group Lasso, Sparse Group Lasso and Trace norm regularizers.