Description: Machine Learning Solutions for Inverse Problems: Part A, Volume 26 in the Handbook of Numerical Analysis, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Data-Driven Approaches for Generalized Lasso Problems, Implicit Regularization of the Deep Inverse Prior via (Inertial) Gradient Flow, Generalized Hardness of Approximation, Hallucinations, and Trustworthiness in Machine Learning for Inverse Problems, Energy-Based Models for Inverse Imaging Problems, Regularization Theory of Stochastic Iterative Methods for Solving Inverse Problems, and more.
Other sections cover Advances in Identifying Differential Equations from Noisy Data Observations, The Complete Electrode Model for Electrical Impedance Tomography: A Comparative Study of Deep Learning and Analytical Methods, Learned Iterative Schemes: Neural Network Architectures for Operator Learning, Jacobian-Free Backpropagation for Unfolded Schemes with Convergence Guarantees, and Operator Learning Meets Inverse Problems: A Probabilistic PerspectiveBrief description: 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.