de los Reyes, Juan Carlos , VILLACIS PROAÑO, DAVID ALEJANDRO
No
IMA J. Appl. Math.
Article
Científica
2
3
1.4
0.389
10/10/2023
001083423200001
In this paper, we investigate the use of bilevel optimization for model learning in variational imaging problems. Bilevel learning is an alternative approach to deep learning methods, which leads to fully interpretable models. However, it requires a detailed analytical insight into the underlying mathematical model. We focus on the bilevel learning problem for total variation models with spatially-and patch dependent parameters. Our study encompasses the directional differentiability of the solution mapping, the derivation of optimality conditions, and the characterization of the Bouligand subdifferential of the solution operator. We also propose a two-phase trust-region algorithm for solving the problem and present numerical tests using the CelebA dataset.