Weighted sparsity regularization for solving the inverse EEG problem: A case study

We study the potential of detecting brain activity in terms of dipoles using weighted sparsity regularization. The work is based on theoretical results that we have proved in previous papers, but it requires modifications to fit into the classical EEG framework. In particular, to represent any dipole at a given position, we only need three basis dipoles with independent directions, but we will demonstrate that it might be beneficial to use more than three dipoles, i.e., a redundant basis/frame. This approach will, in fact, be more in line with the theoretical assumptions needed to guarantee the recovery of a single dipole. We demonstrate through several different experiments that the method does not suffer from the so-called depth bias, and we use standard measures to judge the ability of the method to recover one or two dipole sources. The results show that we do indeed find sparse solutions with relatively small dipole localization errors.