Self-Supervised Learning from Noisy and Incomplete Data

TL;DR

This paper reviews self-supervised learning techniques for inverse problems involving noisy or incomplete data, emphasizing their theoretical foundations and practical applications in imaging, offering an alternative to traditional supervised methods.

Contribution

It provides a comprehensive overview of self-supervised methods for inverse problems, highlighting their theoretical basis and demonstrating their effectiveness in imaging applications.

Findings

Self-supervised methods can effectively solve inverse problems without ground-truth data.

Theoretical analysis supports the validity of self-supervised approaches.

Practical imaging applications show promising results with these methods.

Abstract

Many important problems in science and engineering involve inferring a signal from noisy and/or incomplete observations, where the observation process is known. Historically, this problem has been tackled using hand-crafted regularization (e.g., sparsity, total-variation) to obtain meaningful estimates. Recent data-driven methods often offer better solutions by directly learning a solver from examples of ground-truth signals and associated observations. However, in many real-world applications, obtaining ground-truth references for training is expensive or impossible. Self-supervised learning methods offer a promising alternative by learning a solver from measurement data alone, bypassing the need for ground-truth references. This manuscript provides a comprehensive summary of different self-supervised methods for inverse problems, with a special emphasis on their theoretical underpinnings, and presents practical applications in imaging inverse problems.