Deep Learning for Inverse Problems via Hamilton-Jacobi Equations
Research Paper#Inverse Problems, Deep Learning, Proximal Operators, Hamilton-Jacobi Equations🔬 Research|Analyzed: Jan 3, 2026 16:00•
Published: Dec 29, 2025 19:50
•1 min read
•ArXivAnalysis
This paper introduces a novel deep learning approach for solving inverse problems by leveraging the connection between proximal operators and Hamilton-Jacobi partial differential equations (HJ PDEs). The key innovation is learning the prior directly, avoiding the need for inversion after training, which is a common challenge in existing methods. The paper's significance lies in its potential to improve the efficiency and performance of solving ill-posed inverse problems, particularly in high-dimensional settings.
Key Takeaways
- •Proposes a novel deep learning architecture for inverse problems.
- •Leverages connections between proximal operators and Hamilton-Jacobi equations.
- •Learns the prior directly, avoiding inversion after training.
- •Demonstrates efficiency in high-dimensional settings.
Reference / Citation
View Original"The paper proposes to leverage connections between proximal operators and Hamilton-Jacobi partial differential equations (HJ PDEs) to develop novel deep learning architectures for learning the prior."