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Abstract
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). We show that computing the lower-level optimization problem within the bilevel formulation with a fixed point iteration is a special case of the deep equilibrium framework. We compare both approaches computationally, with a variety of numerical examples for the inverse problems of denoising, inpainting and deconvolution.
Original language | English |
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Number of pages | 25 |
Journal | Numerical Algebra, Control and Optimization |
DOIs | |
Publication status | Published - 31 Jan 2024 |
Keywords
- math.OC
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Dive into the research topics of 'Regularization of Inverse Problems: Deep Equilibrium Models versus Bilevel Learning'. Together they form a unique fingerprint.Projects
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Programme Grant: Mathematics of Deep Learning
Budd, C. (PI) & Ehrhardt, M. (CoI)
Engineering and Physical Sciences Research Council
31/01/22 → 30/01/27
Project: Research council