4 citations · 5 across the 10 of their papers we have counts for
12 papers
Directionally Weighted Total Variation for Inverse Problems
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We study weighted total variation (TV) regularization for inverse problems in which the forward operator has a large null space, a setting in which standard (unweighted) TV is know…
Weighted Group Lasso for a static EEG problem
Ole Løseth Elvetun, Bjørn Fredrik Nielsen, Niranjana Sudheer
We investigate the weighted Group Lasso formulation for the static inverse electroencephalography (EEG) problem, aiming at reconstructing the unknown underlying neuronal sources fr…
Weighted total variation regularization for inverse problems with significant null spaces
Martin Burger, Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically prod…
Weighting operators for sparsity regularization
Ole Løseth Elvetun, Bjørn Fredrik Nielsen, Niranjana Sudheer
Standard regularization methods typically favor solutions which are in, or close to, the orthogonal complement of the null space of the forward operator/matrix . This p…
Fictitious null spaces for improving the solution of injective inverse problems
Ole Løseth Elvetun, Kim Knudsen, Bjørn Fredrik Nielsen
For linear ill-posed problems with nontrivial null spaces, Tikhonov regularization and truncated singular value decomposition (TSVD) typically yield solutions that are close to the…
Identifying the source term in the potential equation with weighted sparsity regularization
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We explore the possibility for using boundary measurements to recover a sparse source term f(x) in the potential equation. Employing weighted sparsity regularization and standard r…
Box constraints and weighted sparsity regularization for identifying sources in elliptic PDEs
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We explore the possibility for using boundary data to identify sources in elliptic PDEs. Even though the associated forward operator has a large null space, it turns out that box c…
Weighted sparsity regularization for source identification for elliptic PDEs
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
This investigation is motivated by PDE-constrained optimization problems arising in connection with electrocardiograms (ECGs) and electroencephalography (EEG). Standard sparsity re…
Modified Tikhonov regularization for identifying several sources
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We study whether a modified version of Tikhonov regularization can be used to identify several local sources from Dirichlet boundary data for a prototypical elliptic PDE. This pape…
A regularization operator for source identification for elliptic PDEs
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We study a source identification problem for a prototypical elliptic PDE from Dirichlet boundary data. This problem is ill-posed, and the involved forward operator has a significan…
Diffuse Interface Methods for Inverse Problems: Case Study for an Elliptic Cauchy Problem
Martin Burger, Ole Loseth Elvetun, Matthias Schlottbom
Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. Thi…
Analysis of the Diffuse Domain Method for second order elliptic boundary value problems
Martin Burger, Ole Løseth Elvetun, Matthias Schlottbom
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental iss…