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

TL;DR

This paper employs bilevel learning to optimize regularization models and their discretization for image deblurring and super-resolution, demonstrating improved restoration performance through learned parameters and filters.

Contribution

It introduces a bilevel learning framework for tuning regularization parameters and discretizations specifically for image restoration tasks, combining variational models with data-driven optimization.

Findings

Effective learning of regularization weights and filters for image restoration

Improved performance in deblurring and super-resolution tasks

Generalization of learned models across multiple image restoration problems

Abstract

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.