Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches
Optimization and Control
2025-06-24 v1
Abstract
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior experiments. This approach enables the integration of data-driven insights into the solution of inverse problems governed by physical models. \emph{Inverse problems}, in general, aim to uncover the \emph{inner mechanisms} of an observed system based on indirect or incomplete measurements. This field has far-reaching applications across various disciplines, such as medical or geophysical imaging, as well as, more broadly speaking, industrial processes where identifying hidden parameters is essential.
Cite
@article{arxiv.2506.17465,
title = {Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches},
author = {Clemens Kirisits and Bochra Mejri and Sergei Pereverzev and Otmar Scherzer and Cong Shi},
journal= {arXiv preprint arXiv:2506.17465},
year = {2025}
}