5 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…