Machine Learning Solutions For Inverse Problems: Part B

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.

• Presents the latest developments in machine learning approaches for solving inverse problems
• Explores modern techniques, including deep learning, generative models, diffusion models, and operator learning
• Covers applications in imaging, tomography, and PDE-based inverse modeling
• Includes theoretical perspectives on stability, approximation hardness, and trustworthiness in AI for inverse problems
• Serves as a comprehensive reference for researchers in numerical analysis, computational mathematics, and scientific computing

Andreas Hauptmann received his PhD in 2017 from the University of Helsinki in Applied Mathematics. He currently holds a position as Academy Research Fellow and Associate Professor (tenure track) of Computational Mathematics at the Research Unit of Mathematical Sciences, University of Oulu, and as Honorary Associate Professor at the Department of Computer Science, University College London. His research interest is in inverse problems and tomographic imaging, with a focus on combining model-based inversion techniques with data-driven methods and the study of their theoretical properties.

Bangti Jin received a PhD in Mathematics from The Chinese University
of Hong Kong, Hong Kong in 2008. Previously, he was Lecturer and Reader, and Professor at Department of Computer Science, University
College London (2014-2022), an assistant professor of Mathematics at the University of California, Riverside (2013–2014), a visiting assistant professor at Texas A&M University (2010–2013), an Alexandre von Humboldt Postdoctoral Researcher at University of Bremen (2009–2010). Currently he is Professor of Mathematics, Global STEM Scholar, at The Chinese University of Hong Kong. His research interests include inverse problems, numerical analysis and machine learning.

Carola-Bibiane Schönlieb graduated from the Institute for Mathematics, University of Salzburg (Austria) in 2004. From 2004 to 2005 she held a teaching position in Salzburg. She received her PhD degree from the University of Cambridge (UK) in 2009. After one year of postdoctoral activity at the University of Göttingen (Germany), she became a Lecturer at Cambridge in 2010, promoted to Reader in 2015 and promoted to Professor in 2018. Since 2011 she is a fellow of Jesus College Cambridge. She currently is Professor of Applied Mathematics (2006) at the University of Cambridge where she is head of the Cambridge Image Analysis group. Her current research interests focus on variational methods, partial differential equations and machine learning for image analysis, image processing and inverse imaging problems.