We provide fast and accurate adaptive algorithms for the spatial resolution of current densities in MEG. We assume that vector components of the current densities possess a sparse expansion with respect to preassigned wavelets. Additionally, different components may also exhibit common sparsity patterns. We model MEG as an inverse problem with joint sparsity constraints, promoting the coupling of non-vanishing components. We show how to compute solutions of the MEG linear inverse problem by iterative thresholded Landweber schemes. The resulting adaptive scheme is fast, robust, and significantly outperforms the classical Tikhonov regularization in resolving sparse current densities. Numerical examples are included. © 2007 Elsevier B.V. All rights reserved.
Fornasier, M., & Pitolli, F. (2008). Adaptive iterative thresholding algorithms for magnetoencephalography (MEG). Journal of Computational and Applied Mathematics, 221(2), 386–395. https://doi.org/10.1016/j.cam.2007.10.048