Adaptive iterative thresholding algorithms for magnetoencephalography (MEG)

Authors:
Massimo Fornasier;Francesca Pitolli
Affiliations:
Program in Applied and Computational Mathematics, Princeton University, Fine Hall, Washington Road, 08544-1000 Princeton, NJ, USA;Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Universití di Roma "La Sapienza", Via A. Scarpa 16, I-00161 Roma, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

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.