Volume 58, pp. 486-516, 2023.
A computational framework for edge-preserving regularization in dynamic inverse problems
Mirjeta Pasha, Arvind K. Saibaba, Silvia Gazzola, Malena I. Español, and Eric de Sturler
Abstract
We devise efficient methods for dynamic inverse problems, where both the quantities of interest and the forward operator (measurement process) may change in time. Our goal is to solve for all the quantities of interest simultaneously. We consider large-scale ill-posed problems made more challenging by their dynamic nature and, possibly, by the limited amount of available data per measurement step. To alleviate these difficulties, we apply a unified class of regularization methods that enforce simultaneous regularization in space and time (such as edge enhancement at each time instant and proximity at consecutive time instants) and achieve this with low computational cost and enhanced accuracy. More precisely, we develop iterative methods based on a majorization-minimization (MM) strategy with quadratic tangent majorant, which allows the resulting least-squares problem with a total variation regularization term to be solved with a generalized Krylov subspace (GKS) method; the regularization parameter can be determined automatically and efficiently at each iteration. Numerical examples from a wide range of applications, such as limited-angle computerized tomography (CT), space-time image deblurring, and photoacoustic tomography (PAT), illustrate the effectiveness of the described approaches.
Full Text (PDF) [3.5 MB], BibTeX
Key words
dynamic inversion, time-dependence, edge-preservation, majorization-minimization, regularization, generalized Krylov subspaces, image deblurring, photoacoustic tomography, computerized tomography
AMS subject classifications
65F10, 65F22, 65F50
Links to the cited ETNA articles
| [30] | Vol. 40 (2013), pp. 452-475 Silvia Gazzola and Paolo Novati: Multi-parameter Arnoldi-Tikhonov methods |
Additional resources for this document
| Additional files |
< Back