Data-Consistent Learning of Inverse Problems

2026-01-19

AI Summary

This work addresses the ill-posed nature of inverse problems, which often leads to non-unique and unstable solutions. To this end, we propose a deep learning-based reconstruction framework that integrates spatial-domain neural networks, data consistency constraints, and classical regularization, explicitly embedding the measurement model into the network architecture. The proposed method not only inherits the convergence guarantees from traditional regularization theory but also leverages data-driven learning to enhance visual fidelity in reconstructions. The resulting model is theoretically provable in terms of convergence and, in practice, achieves a balance between stability and high-quality output, thereby unifying theoretical reliability with perceptual performance.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced flexibility or visual quality. Learned reconstruction methods, such as convolutional neural networks, can produce visually compelling results, yet they typically lack rigorous theoretical guarantees. DC (DC) networks address this gap by enforcing the measurement model within the network architecture. In particular, null-space networks combined with a classical regularization method as an initial reconstruction define a convergent regularization method. This approach preserves the theoretical reliability of classical schemes while leveraging the expressive power of data-driven learning, yielding reconstructions that are both accurate and visually appealing.

Problem

• inverse problems
• ill-posedness
• regularization
• data-driven learning
• theoretical guarantees

Innovation

• Data-Consistent Learning
• Inverse Problems
• Null-Space Networks
• Convergent Regularization
• Measurement Model Embedding