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.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. List of contributors - p. xv 7. Preface - p. xix 8. Chapter 1: Diffusion models for inverse problems - p. 1 9. Chapter 2: Solving imaging inverse problems using plug-and-play denoisers: regularization and optimization perspectives - p. 41 10. Chapter 3: Learning regularization functionals for inverse problems: a comparative study - p. 85 11. Chapter 4: Deep image prior for computed tomography reconstruction - p. 137 12. Chapter 5: Self-supervised deep learning for inverse imaging problems - p. 173 13. Chapter 6: Bilevel learning for inverse problems: single-level reformulations and consequences - p. 213 14. Chapter 7: Operator learning meets inverse problems - p. 253 15. Chapter 8: Learned iterative networks - p. 341 16. Chapter 9: A unified framework for lifted training and inversion approaches - p. 425 17. Chapter 10: Data-consistent learning of inverse problems - p. 487 18. Chapter 11: On generalized hardness of approximation, hallucinations, instability, and trustworthiness in AI for inverse problems - p. 507 19. Chapter 12: Numerical analysis of unsupervised learning approaches for parameter identification in PDEs - p. 543 20. Chapter 13: What can one expect when solving PDEs using shallow neural networks? - p. 621 21. Chapter 14: Data selection: at the interface of PDE-based inverse problem and randomized linear algebra - p. 669 22. Chapter 15: Coupling deep learning with full waveform inversion - p. 715
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.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. List of contributors - p. xv 7. Preface - p. xix 8. Chapter 1: Diffusion models for inverse problems - p. 1 9. Chapter 2: Solving imaging inverse problems using plug-and-play denoisers: regularization and optimization perspectives - p. 41 10. Chapter 3: Learning regularization functionals for inverse problems: a comparative study - p. 85 11. Chapter 4: Deep image prior for computed tomography reconstruction - p. 137 12. Chapter 5: Self-supervised deep learning for inverse imaging problems - p. 173 13. Chapter 6: Bilevel learning for inverse problems: single-level reformulations and consequences - p. 213 14. Chapter 7: Operator learning meets inverse problems - p. 253 15. Chapter 8: Learned iterative networks - p. 341 16. Chapter 9: A unified framework for lifted training and inversion approaches - p. 425 17. Chapter 10: Data-consistent learning of inverse problems - p. 487 18. Chapter 11: On generalized hardness of approximation, hallucinations, instability, and trustworthiness in AI for inverse problems - p. 507 19. Chapter 12: Numerical analysis of unsupervised learning approaches for parameter identification in PDEs - p. 543 20. Chapter 13: What can one expect when solving PDEs using shallow neural networks? - p. 621 21. Chapter 14: Data selection: at the interface of PDE-based inverse problem and randomized linear algebra - p. 669 22. Chapter 15: Coupling deep learning with full waveform inversion - p. 715
