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Data-driven Models in Inverse Problems
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Edited by:
Tatiana A. Bubba
Language:
English
Published/Copyright:
2025
About this book
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.
- Combines classical approaches in regularization theory with deep neural networks.
- Describes the Mathematical aspects of data-driven inverse problems.
- Discusses specific applications of data-driven methods in inverse problems.
Author / Editor information
long Bio (mandatory for Amazon Top Titles)
Topics
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Frontmatter
I -
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Preface
V -
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Contents
VII - Part I: Mathematical aspects of data-driven methods in inverse problems
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On optimal regularization parameters via bilevel learning
1 -
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Learned regularization for inverse problems
39 -
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Inverse problems with learned forward operators
73 -
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Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging
107 -
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Learned reconstruction methods for inverse problems: sample error estimates
163 -
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Statistical inverse learning problems with random observations
201 -
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General regularization in covariate shift adaptation
245 - Part II: Applications of data-driven methods in inverse problems
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Analysis of generalized iteratively regularized Landweber iterations driven by data
273 -
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Integration of model- and learning-based methods in image restoration
303 -
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Dynamic computerized tomography using inexact models and motion estimation
331 -
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Deep Bayesian inversion
359 -
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Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography
413 -
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Electrical impedance tomography: a fair comparative study on deep learning and analytic-based approaches
437 -
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Classification with neural networks with quadratic decision functions
471 -
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Index
495
Publishing information
Pages and Images/Illustrations in book
eBook published on:
November 18, 2024
eBook ISBN:
9783111251233
Hardcover published on:
November 18, 2024
Hardcover ISBN:
9783111250038
Pages and Images/Illustrations in book
Front matter:
8
Main content:
500
Illustrations:
36
Coloured Illustrations:
80
Keywords for this book
Deep neural networks; Regularization of inverse problems; Computerized imaging; Numerical methods for inverse problems; Signal processing
Audience(s) for this book
Institutional libraries and researchers working in applied mathematics, and data science.
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
