The Regularized Orthogonal Functional Matching Pursuit for Ill-Posed Inverse Problems

DOI10.1137/141000695zbMath1382.65162OpenAlexW2258628301MaRDI QIDQ5745017

Volker Michel, Roger Telschow

Publication date: 11 February 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/141000695

zbMATH Keywords

inverse problemregularizationmultiresolution analysisspheregreedy algorithmscattered datanonlinear approximationill-posedmatching pursuitdownward continuation

Mathematics Subject Classification ID

Inverse problems in geophysics (86A22) Numerical methods for inverse problems for integral equations (65R32) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (10)

A unified approach to scalar, vector, and tensor Slepian functions on the sphere and their construction by a commuting operator ⋮ On the convergence theorem for the regularized functional matching pursuit (RFMP) algorithm ⋮ Vectorial Slepian Functions on the Ball ⋮ A greedy algorithm for nonlinear inverse problems with an application to nonlinear inverse gravimetry ⋮ On the null space of a class of Fredholm integral equations of the first kind ⋮ A first approach to learning a best basis for gravitational field modelling ⋮ Electro-magnetoencephalography for a spherical multiple-shell model: novel integral operators with singular-value decompositions ⋮ The regularized weak functional matching pursuit for linear inverse problems ⋮ Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods ⋮ Regularized functional matching pursuit for the spherical multiple-shell electro-magnetoencephalography problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• An integrated wavelet concept of physical geodesy
• Spherical spline interpolation - basic theory and computational aspects
• On the computation of nonnegative quadrature weights on the sphere
• A survey on spherical spline approximation
• Lectures on constructive approximation. Fourier, spline, and wavelet methods on the real line, the sphere, and the ball
• Spherical wavelet transform and its discretization
• Spherical harmonics
• Sparse regularization of inverse gravimetry—case study: spatial and temporal mass variations in South America
• Spline Interpolation and Smoothing on the Sphere
• On spherical spline interpolation and approximation
• An iterative method for solving incorrectly posed problems
• Regularization wavelets and multiresolution
• Matching pursuits with time-frequency dictionaries
• Kernel matching pursuit

This page was built for publication: The Regularized Orthogonal Functional Matching Pursuit for Ill-Posed Inverse Problems