Variational regularisation for inverse problems with imperfect forward operators and general noise models
Year: 2020
Type: article
Abstract: We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and convex duality for general data fidelity terms and regularisation functionals. Both for a priori and a posteriori parameter choice rules, we obtain convergence rates of the regularised solutions in terms of Bregman distances. Our results apply to fidelity terms such as Wasserstein distances, φ -divergences, norms, as well as sums and infimal convolutions of those.
Source: Inverse Problems
Authors: Leon Bungert, Martin Burger, Yury Korolev, Carola-Bibiane Schönlieb
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
Awards: G1018969006, G1755984640, Nonlocal Methods for Arbitrary Data Sources, Robust and Efficient Analysis Approaches of Remote Imagery for Assessing Population and Forest Health in India, G2978676218, G2999167548, CHallenges in Preservation of Structure, Regularisation theory in the data driven setting, Verbundprojekt 05M2016 - MED4D: Dynamische Medizinische Bildgebung: Modellierung und Analyse medizinischer Daten für verbesserte Diagnose, Überwachung und Arzneimittelentwicklung - Teilprojekt 1, Efficient computational tools for inverse imaging problems, G6024586586, G6497358115, EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging, G6935067837, PET++: Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation, G8438671910
OpenAlex ID: W3032077587