Machine Learned Regularisation for Solving Inverse Problems

Explore machine learning-based regularization techniques for solving inverse problems in this 55-minute lecture by Carola Schönlieb at the Hausdorff Center for Mathematics. Delve into the world of ill-posed inverse problems and learn how regularization methods can be used to reconstruct unknown physical quantities from indirect measurements. Compare classical handcrafted approaches like Tikhonov regularization and total variation with modern data-driven techniques utilizing deep neural networks. Examine unsupervised and deeply learned convex regularizers, and their applications in image reconstruction from tomographic and blurred measurements. Gain insights into the limitations of traditional methods and the potential of machine learning in this field. Conclude with a discussion on open mathematical problems and future directions in machine learned regularization for inverse problems.

Intro
Linear inverse problems
Variation regularisation
Applications
Limitations
Datadriven approaches
Total variation regularisation
How have people thought about this
Postprocessing
Framework
Learning a Regularizer
Joint Work
Optimality Criteria
Summary