REGULARIZATION OF INVERSE PROBLEMS: DEEP EQUILIBRIUM MODELS VERSUS BILEVEL LEARNING

被引:0
|
作者
Riccio, Danilo [1 ]
Ehrhardt, Matthias j. [2 ]
Benning, Martin [3 ]
机构
[1] Queen Mary Univ London, London, England
[2] Univ Bath, Bath, England
[3] UCL, London, England
来源
NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2023年
基金
英国工程与自然科学研究理事会;
关键词
Key words and phrases. Deep learning; bilevel optimization; variational regularization; regu; larization; inverse problems; bilevel learning; deep equilibrium;
D O I
10.3934/naco.2023026
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
. 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 [32]. 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 [3] that has recently been introduced in the context of inverse problems [13]. 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.
引用
收藏
页数:25
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