Calculus of Variations and Geometric Measure Theory

M. Carioni - S. Mukherjee - Hong Ye Tan - J. Tang

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

created by carioni on 23 Feb 2024

[BibTeX]

preprint

Inserted: 23 feb 2024
Last Updated: 23 feb 2024

Year: 2023

ArXiv: 2311.08972 PDF

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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