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Full Description
Machine Learning Solutions for Inverse Problems: Part B, Volume 27 in the Handbook of Numerical Analysis, continues the exploration of emerging approaches at the intersection of machine learning and inverse problem theory. This volume presents a collection of chapters addressing a wide range of contemporary topics, including deep image prior methods for computed tomography, data-consistent learning strategies, and unified frameworks for training and inversion in machine learning-based reconstruction methods.
Additional chapters examine learned regularization techniques, generative models for inverse problems, and the integration of deep learning with traditional computational frameworks such as full waveform inversion and PDE-based inverse modeling. The volume also discusses advances in self-supervised learning, data selection strategies, plug-and-play denoising methods, and diffusion models for solving imaging inverse problems.
Further contributions explore neural network representations, operator learning, and learned iterative schemes, along with theoretical perspectives on stability, approximation hardness, hallucinations, and trustworthiness in AI-driven inverse problem methodologies. Together, these chapters provide a comprehensive overview of current developments in machine learning approaches to inverse problems, offering valuable insights for researchers in numerical analysis, computational mathematics, and scientific computing.
Contents
1. Deep Image Prior for Computed Tomography
2. A Unified Framework for Lifted Training and Inversion Approaches
3. Learned Regularization for Inverse Problems: Potentials and Challenges of Generative Models
4. Learned Regularization for Inverse Problems: Potentials and Challenges of Generative Models
5. Data Consistent Learning of Inverse Problems
6. Yet to Be Decided
7. Self-Supervised Deep Learning for Inverse Imaging Problems
8. Data Selection: At the Interface of PDE-Based Inverse Problems and Randomized Linear Algebra
9. Learning Regularization Functionals for Inverse Problems: A Comparative Study
10. Coupling Deep Learning with Full Waveform Inversion
11. Solving Imaging Inverse Problems Using Plug-and-Play Denoisers: Regularization and Optimization Perspectives
12. Diffusion Models for Inverse Problems
13. Neural Networks for Inverse Problems: From Representation to Learning Dynamics
14. Numerical Analysis of Unsupervised Learning Approaches for Parameter Identification in PDEs
15. On Generalised Hardness of Approximation, Hallucinations, Instability and Trustworthiness in AI for Inverse Problems
16. Operator Learning Meets Inverse Problems
17. Learned Iterative Networks: An Operator Learning Perspective
