Adaptive Iterative Thresholding Algorithms for Magnetoenceophalography (MEG)

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 coupling of non-vanishing components. We show how to compute solutions of the MEG linear inverse problem by iterative thresholded Landweber schemes. At each iteration an adaptive application of a compressed matrix associated to the Biot-Savart operator in wavelet coordinates is introduced. The resulting adaptive scheme is fast, robust, and significantly outperforms the classical Tikhonov regularization in resolving sparse current densities. Numerical examples are included. AMS subject classification: 65J22, 65K10, 65T60, 52A41, 49M30, 68U10