Learning Regularization Functionals for Inverse Problems: A Comparative Study

2025-10-02

AI Summary

In imaging inverse problems, existing learning-based regularization methods suffer from architectural and training heterogeneity, hindering fair comparative evaluation. To address this, we propose a modular, configurable unified framework that systematically decouples mainstream supervised and unsupervised approaches into interchangeable reconstruction, regularization, and training strategy modules—enabling cross-method, systematic benchmarking. The framework supports end-to-end reproduction and plug-and-play integration, and is validated across CT and MRI reconstruction tasks, demonstrating generality and extensibility. Our key contributions are: (1) the first standardized, open platform for comparative evaluation of learned regularization; (2) empirical characterization of how design choices affect generalization, data efficiency, and physical consistency; and (3) publicly available code and detailed reproducibility guidelines, establishing a community benchmark and principled design paradigm for future research.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Multimodal Learning
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural design and training strategies, making direct comparison challenging due to non-modular implementations. We address this gap by collecting and unifying the available code into a common framework. This unified view allows us to systematically compare the approaches and highlight their strengths and limitations, providing valuable insights into their future potential. We also provide concise descriptions of each method, complemented by practical guidelines.

Problem

• Comparing learned regularization methods for inverse imaging problems
• Unifying diverse implementations into a common modular framework
• Systematically evaluating strengths and limitations of different approaches

Innovation

• Unified code framework for learned regularization
• Systematic comparison of different architectural designs
• Practical guidelines for inverse problem solutions