Regularized functional matching pursuit for the spherical multiple-shell electro-magnetoencephalography problem

DOI10.1553/etna_vol57s153zbMath1505.92116OpenAlexW4296373327MaRDI QIDQ2100870

Sarah Leweke, Volker Michel

Publication date: 25 November 2022

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1553/etna_vol57s153

zbMATH Keywords

Sobolev spacesintegral equationinverse problemsill-posed problemsregularization methodselectroencephalographygreedy algorithmsmagnetoencephalographyregularized functional matching pursuit

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Numerical methods for ill-posed problems for integral equations (65R30) Numerical methods for inverse problems for integral equations (65R32)

Uses Software

• GitHub

Cites Work

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• Spline multiresolution and numerical results for joint gravitation and normal-mode inversion with an outlook on sparse regularisation
• A non-linear approximation method on the sphere
• Comparing parameter choice methods for regularization of ill-posed problems
• Spherical functions of mathematical geosciences. A scalar, vectorial, and tensorial setup
• Computing Fourier transforms and convolutions on the 2-sphere
• On the convergence theorem for the regularized functional matching pursuit (RFMP) algorithm
• Lectures on constructive approximation. Fourier, spline, and wavelet methods on the real line, the sphere, and the ball
• Regularization of geopotential determination from satellite data by variance components
• A first approach to learning a best basis for gravitational field modelling
• The regularized weak functional matching pursuit for linear inverse problems
• A parameter choice strategy for the inversion of multiple observations
• Wavelet decomposition of spherical vector fields with respect to sources
• On the null space of a class of Fredholm integral equations of the first kind
• Sparse regularization of inverse gravimetry—case study: spatial and temporal mass variations in South America
• Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods
• The Accuracy of Floating Point Summation
• Special Functions in Mathematical Geosciences: An Attempt at a Categorization
• Matching pursuits with time-frequency dictionaries
• Geomathematics
• Vector-valued spline method for the spherical multiple-shell electro-magnetoencephalography problem
• Electro-magnetoencephalography for a spherical multiple-shell model: novel integral operators with singular-value decompositions
• Pseudo-differential Operators, Cubature and Equidistribution on the 3D ball: An Approach Based on Orthonormal Basis Systems
• Electro-magneto-encephalography for the three-shell model: numerical implementation via splines for distributed current in spherical geometry
• Aggregation of regularized solutions from multiple observation models
• The Regularized Orthogonal Functional Matching Pursuit for Ill-Posed Inverse Problems
• Measure and integration theory. Transl. from the German by Robert B. Burckel
• Kernel matching pursuit

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