Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging

• URL: http://arxiv.org/abs/2311.08972v2
• Date: Wed, 29 Nov 2023 09:57:06 GMT
• Title: Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging
• Authors: Marcello Carioni, Subhadip Mukherjee, Hong Ye Tan, Junqi Tang
• Abstract summary: We review theoretically principled unsupervised learning schemes for solving imaging inverse problems. We focus on methods rooted in optimal transport and convex analysis. We give an overview of a recent line of works on provably convergent learned optimization algorithms.
• Score: 6.202226277935329
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction operators even when paired high-quality training data is scarcely available. In this chapter, we review theoretically principled unsupervised learning schemes for solving imaging inverse problems, with a particular focus on methods rooted in optimal transport and convex analysis. We begin by reviewing the optimal transport-based unsupervised approaches such as the cycle-consistency-based models and learned adversarial regularization methods, which have clear probabilistic interpretations. Subsequently, we give an overview of a recent line of works on provably convergent learned optimization algorithms applied to accelerate the solution of imaging inverse problems, alongside their dedicated unsupervised training schemes. We also survey a number of provably convergent plug-and-play algorithms (based on gradient-step deep denoisers), which are among the most important and widely applied unsupervised approaches for imaging problems. At the end of this survey, we provide an overview of a few related unsupervised learning frameworks that complement our focused schemes. Together with a detailed survey, we provide an overview of the key mathematical results that underlie the methods reviewed in the chapter to keep our discussion self-contained.

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