Variational Regularization for Systems of Inverse Problems

Variational Regularization for Systems of Inverse Problems PDF

Author: Richard Huber

Publisher:

Published: 2019

Total Pages: 136

ISBN-13: 9783658253912

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Tikhonov regularization is a cornerstone technique in solving inverse problems with applications in countless scientific fields. Richard Huber discusses a multi-parameter Tikhonov approach for systems of inverse problems in order to take advantage of their specific structure. Such an approach allows to choose the regularization weights of each subproblem individually with respect to the corresponding noise levels and degrees of ill-posedness. Contents General Tikhonov Regularization Specific Discrepancies Regularization Functionals Application to STEM Tomography Reconstruction Target Groups Researchers and students in the field of mathematics Experts in the areas of mathematics, imaging, computer vision and nanotechnology The Author Richard Huber wrote his master's thesis under the supervision of Prof. Dr. Kristian Bredies at the Institute for Mathematics and Scientific Computing at Graz University, Austria.

Variational Regularization for Systems of Inverse Problems

Variational Regularization for Systems of Inverse Problems PDF

Author: Richard Huber

Publisher: Springer

Published: 2019-02-14

Total Pages: 136

ISBN-13: 3658253908

DOWNLOAD EBOOK →

Tikhonov regularization is a cornerstone technique in solving inverse problems with applications in countless scientific fields. Richard Huber discusses a multi-parameter Tikhonov approach for systems of inverse problems in order to take advantage of their specific structure. Such an approach allows to choose the regularization weights of each subproblem individually with respect to the corresponding noise levels and degrees of ill-posedness.

Nanoscale Photonic Imaging

Nanoscale Photonic Imaging PDF

Author: Tim Salditt

Publisher: Springer Nature

Published: 2020-06-09

Total Pages: 634

ISBN-13: 3030344134

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This open access book, edited and authored by a team of world-leading researchers, provides a broad overview of advanced photonic methods for nanoscale visualization, as well as describing a range of fascinating in-depth studies. Introductory chapters cover the most relevant physics and basic methods that young researchers need to master in order to work effectively in the field of nanoscale photonic imaging, from physical first principles, to instrumentation, to mathematical foundations of imaging and data analysis. Subsequent chapters demonstrate how these cutting edge methods are applied to a variety of systems, including complex fluids and biomolecular systems, for visualizing their structure and dynamics, in space and on timescales extending over many orders of magnitude down to the femtosecond range. Progress in nanoscale photonic imaging in Göttingen has been the sum total of more than a decade of work by a wide range of scientists and mathematicians across disciplines, working together in a vibrant collaboration of a kind rarely matched. This volume presents the highlights of their research achievements and serves as a record of the unique and remarkable constellation of contributors, as well as looking ahead at the future prospects in this field. It will serve not only as a useful reference for experienced researchers but also as a valuable point of entry for newcomers.

Handbook of Mathematical Methods in Imaging

Handbook of Mathematical Methods in Imaging PDF

Author: Otmar Scherzer

Publisher: Springer Science & Business Media

Published: 2010-11-23

Total Pages: 1626

ISBN-13: 0387929193

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The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Discrete Inverse Problems

Discrete Inverse Problems PDF

Author: Per Christian Hansen

Publisher: SIAM

Published: 2010-01-01

Total Pages: 220

ISBN-13: 089871883X

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This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.

Convergence Rates for Variational Regularization of Statistical Inverse Problems

Convergence Rates for Variational Regularization of Statistical Inverse Problems PDF

Author: Benjamin Sprung

Publisher:

Published: 2020

Total Pages: 0

ISBN-13:

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We consider inverse problems with statistical (noisy) data. By applying regularization methods one can approximate the true solution of the inverse problem by a regularized solution. In this thesis we show convergence rates of the regularized solution to the true solution as the noise tends to zero under so called source conditions on the true solution. Recently variational source conditions (VSCs) have become increasingly popular, due to their generality. However, they have the disadvantage that they only give optimal rates for low smoothness of the true solution. For this reason a second ...

Variational Methods in Imaging

Variational Methods in Imaging PDF

Author: Otmar Scherzer

Publisher: Springer Science & Business Media

Published: 2008-09-26

Total Pages: 323

ISBN-13: 0387692770

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This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.

Inverse Problems and Related Topics

Inverse Problems and Related Topics PDF

Author: Jin Cheng

Publisher: Springer Nature

Published: 2020-02-04

Total Pages: 310

ISBN-13: 9811515921

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This volume contains 13 chapters, which are extended versions of the presentations at International Conference on Inverse Problems at Fudan University, Shanghai, China, October 12-14, 2018, in honor of Masahiro Yamamoto on the occasion of his 60th anniversary. The chapters are authored by world-renowned researchers and rising young talents, and are updated accounts of various aspects of the researches on inverse problems. The volume covers theories of inverse problems for partial differential equations, regularization methods, and related topics from control theory. This book addresses a wide audience of researchers and young post-docs and graduate students who are interested in mathematical sciences as well as mathematics.