عنوان

Variational regularization for systems of inverse problems :

(Number (ISBN

3658253908

(Number (ISBN

9783658253905

Erroneous ISBN

3658253894

Erroneous ISBN

9783658253899

Title Proper

Variational regularization for systems of inverse problems :

General Material Designation

[Book]

Other Title Information

Tikhonov regularization with multiple forward operators /

First Statement of Responsibility

Richard Huber.

Place of Publication, Distribution, etc.

Wiesbaden, Germany :

Name of Publisher, Distributor, etc.

Springer Spektrum,

Date of Publication, Distribution, etc.

2019.

Specific Material Designation and Extent of Item

1 online resource (ix, 136 pages) :

Other Physical Details

illustrations

Series Title

BestMasters,

ISSN of Series

2625-3577

Text of Note

Includes bibliographical references.

Text of Note

Intro; Acknowledgements; Contents; List of Figures; I. Introduction; I.1. Motivation; I.2. Mathematical Foundation; I.2.1 Topologies; I.2.2 Normed Vector Spaces; I.2.3 Measure Theory; I.2.4 Convex Analysis; II. General Tikhonov Regularisation; II. 1. Single-Data Tikhonov Regularisation; II. 1.1 Existence and Stability; II. 1.2 Convergence; II. 2. Multi-Data Tikhonov Regularisation; II. 2.1 Preliminaries; II. 2.2 Parameter Choices for Vanishing Noise; II. 2.3 Convergence rates; III. Specific Discrepancies; III. 1. Norm Discrepancies; III. 1.1 Classical Norms; III. 1.2 Subnorms

Text of Note

III. 2. Kullback-Leibler DivergenceIII. 2.1 Motivation; III. 2.2 Basic Properties; III. 2.3 Continuity Results; III. 2.4 Applicability as a Discrepancy; IV. Regularisation Functionals; IV. 1. Regularisation with Norms and Closed Operators; IV. 2. Total Deformation; IV. 2.1 Symmetric Tensor Fields; IV. 2.2 Tensor Fields of Bounded Deformation; IV. 3. Total Generalised Variation; IV. 3.1 Basic Properties; IV. 3.2 Topological Properties; IV. 3.3 Total Generalised Variation of Vector-Valued Functions; IV. 4. TGV Regularisation in a Linear Setting; V. Application to STEM Tomography Reconstruction

Text of Note

v. 1. The Radon TransformV. 1.1 Deriving the Radon Transform; V.1.2 Analytical Properties; V.1.3 Filtered Backprojection; V.2. Tikhonov Approach to Multi-Spectra STEM Tomography Reconstruction; V.2.1 Continuous Tikhonov Problem for STEM Tomography Reconstruction; V.2.2 Discretisation Scheme; V.2.3 Primal-Dual Optimisation Algorithm; V.2.4 STEM Tomography Reconstruction Algorithm; V.3. Discussion of Numerical Results; V.3.1 Preprocessing; V.3.2 Synthetic Experiments; V.3.3 Reconstruction of Single-Data HAADF Signals; V.3.4 STEM Multi-Spectral Reconstructions; Summary; Bibliography

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Text of Note

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.

Title

Variational regularization for systems of inverse problems.

International Standard Book Number

9783658253899

Inverse problems (Differential equations)

Inverse problems (Differential equations)

Number

Edition

Class number

Huber, Richard

Date of Transaction

20200823183737.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y