"Cortical Wavelets for the M/EEG Inverse Problem"Verrier, ClémentThe M/EEG (magneto or electroencephalography) inverse problem comes from electromagnetic brain imaging. The goal is to reconstitute an electric current density on the surface of the cortex from external measurements recorded by sensors outside the skull. It is severely ill-posed, and requires to introduce a priori information on the sources, i.e. the current density to be estimated. This immediately leads one to wonder what is the most relevant priors to use. In this paper we describe a wavelet-based variational formulation, involving penalization that promotes sparsity in the wavelet domain. We propose a construction of spatial wavelet bases defined on the cortical surface, that combines random multiresolution partitions of the surface with the lifting scheme for the construction of wavelets. A motivation for such penalizations originates from image processing, where it is known that $\ell^1$ penalization of wavelet coefficients promotes "cartoon"-type behavior on reconstructed images, which may be physiologically relevant for the considered application. |
| http://univie.ac.at/projektservice-mathematik/e/talks/Verrier_2021-06_bare_conf_ICCHA.pdf |
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