Structured sparse-low rank matrix factorization for the EEG inverse problem

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 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 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.