Bubba T. Data-driven Models in Inverse Problems 2025

Textbook in PDF format

Advances in learning-based methods are revolutionizing several fields in applied mathematics, including inverse problems, resulting in a major paradigm shift towards data-driven approaches. This volume, which is inspired by this cutting-edge area of research, brings together contributors from the inverse problem community and shows how to successfully combine model- and data-driven approaches to gain insight into practical and theoretical issues.
Preface
Mathematical aspects of data-driven methods in inverse problems
On optimal regularization parameters via bilevel learning
Learned regularization for inverse problems
Inverse problems with learned forward operators
Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging
Learned reconstruction methods for inverse problems: sample error estimates
Statistical inverse learning problems with random observations
General regularization in covariate shift adaptation
Applications of data-driven methods in inverse problems
Analysis of generalized iteratively regularized Landweber iterations driven by data
Integration of model- and learning-based methods in image restoration
Dynamic computerized tomography using inexact models and motion estimation
Deep Bayesian inversion
Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography
Electrical impedance tomography: a fair comparative study on deep learning and analytic-based approaches
Classification with neural networks with quadratic decision functions
Index