Regularization of Inverse Problems: Deep Equilibrium Models versus Bilevel Learning

Understand

Variational regularization methods are commonly used to approximate solutions of inverse problems.

• In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert model (Roth and Black, 2009).
• Training the parameters of such data-driven methods can be formulated as a bilevel optimization problem.
• In this paper, we compare the framework of bilevel learning for the training of data-driven variational regularization models with the novel framework of deep equilibrium models (Bai, Kolter, and Koltun, 2019) that has recently been introduced in the context of inverse problems (Gilton, Ongie, and Willett, 2021).