Bilevel learning of regularization models and their discretization for image deblurring and super-resolution

• Main Authors: Bubba, Tatiana A, Calatroni, Luca, Catozzi, Ambra, Crisci, Serena, Pock, Thomas, Pragliola, Monica, Rautio, Siiri, Riccio, Danilo, Sebastiani, Andrea
• Format: Journal Article
• Language: English
• Published: 20-02-2023
• Subjects: Computer Science - Numerical Analysis; Mathematics - Numerical Analysis; Mathematics - Optimization and Control
• DOI: 10.48550/arxiv.2302.10056

Bilevel learning is a powerful optimization technique that has extensively
been employed in recent years to bridge the world of model-driven variational
approaches with data-driven methods. Upon suitable parametrization of the
desired quantities of interest (e.g., regularization terms or discretization
filters), such approach computes optimal parameter values by solving a nested
optimization problem where the variational model acts as a constraint. In this
work, we consider two different use cases of bilevel learning for the problem
of image restoration. First, we focus on learning scalar weights and
convolutional filters defining a Field of Experts regularizer to restore
natural images degraded by blur and noise. For improving the practical
performance, the lower-level problem is solved by means of a gradient descent
scheme combined with a line-search strategy based on the Barzilai-Borwein rule.
As a second application, the bilevel setup is employed for learning a
discretization of the popular total variation regularizer for solving image
restoration problems (in particular, deblurring and super-resolution).
Numerical results show the effectiveness of the approach and their
generalization to multiple tasks.