Davoli, E., Fonseca, I., & Liu, P. (2023). Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme. Journal of Nonlinear Science, 33(3), Article 41. https://doi.org/10.1007/s00332-023-09902-4
Γ-convergence; First order differential operators; Image processing; Optimal training scheme
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Abstract:
A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers TGV² and NsTGV². Optimal parameters and regularizers are identified, and the existence of a solution for any given set of training imaging data is proved by Γ-convergence under a conditional uniform bound on the trace constant of the operators and a finite-null-space condition. Some first examples and numerical results are given.
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Project title:
Hochkontrast-Materialien in Plastizität und Magnetismus: V662-N32 (FWF - Österr. Wissenschaftsfonds) Smarte Materialien: Geometrie, Nichtlokalität, Chiralität: Y1292-N (FWF - Österr. Wissenschaftsfonds) Herausforderungen in der Modellierung grosser Verformungen: I 4052 (FWF - Österr. Wissenschaftsfonds)
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Project (external):
Austrian Science Fund (FWF) BMBWF National Science Foundation National Science Foundation Centre of Mathematical Imaging and Healthcare
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Project ID:
F 65 CZ04/2019 DMS-1411646 DMS-1906238 EP/N014588/1
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Research Areas:
Modeling and Simulation: 50% Fundamental Mathematics Research: 50%
CC BY 4.0
