Interpretable model learning in variational imaging: a bilevel optimization approach

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 ma...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 89; no. 1; pp. 85 - 122
Main Authors De los Reyes, Juan Carlos, Villacís, David
Format Journal Article
LanguageEnglish
Published Oxford University Press 21.06.2024
Subjects
49K99
68U10
68T99
65K10
90C33
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Summary: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.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxad024