Time-dependent Problems in Imaging and Parameter Identification

1. Front Matter

   Pages i-xiv

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2. Joint Phase Reconstruction and Magnitude Segmentation from Velocity-Encoded MRI Data

   • Veronica Corona, Martin Benning, Lynn F. Gladden, Andi Reci, Andrew J. Sederman, Carola-Bibiane Schönlieb

   Pages 1-24

3. Dynamic Inverse Problems for the Acoustic Wave Equation

   • Thies Gerken

   Pages 25-49

4. Motion Compensation Strategies in Tomography

   • Bernadette N. Hahn

   Pages 51-83

5. Microlocal Properties of Dynamic Fourier Integral Operators

   • Bernadette N. Hahn, Melina-L. Kienle Garrido, Eric Todd Quinto

   Pages 85-120

6. The Tangential Cone Condition for Some Coefficient Identification Model Problems in Parabolic PDEs

   • Barbara Kaltenbacher, Tram Thi Ngoc Nguyen, Otmar Scherzer

   Pages 121-163

7. Sequential Subspace Optimization for Recovering Stored Energy Functions in Hyperelastic Materials from Time-Dependent Data

   • Rebecca Klein, Thomas Schuster, Anne Wald

   Pages 165-190

8. Joint Motion Estimation and Source Identification Using Convective Regularisation with an Application to the Analysis of Laser Nanoablations

   • Lukas F. Lang, Nilankur Dutta, Elena Scarpa, Bénédicte Sanson, Carola-Bibiane Schönlieb, Jocelyn Étienne

   Pages 191-227

9. Quantitative OCT Reconstructions for Dispersive Media

   • Peter Elbau, Leonidas Mindrinos, Leopold Veselka

   Pages 229-266

10. Review of Image Similarity Measures for Joint Image Reconstruction from Multiple Measurements

    • Ming Jiang

    Pages 267-286

11. Holmgren-John Unique Continuation Theorem for Viscoelastic Systems

    • Maarten V. de Hoop, Ching-Lung Lin, Gen Nakamura

    Pages 287-301

12. Tomographic Reconstruction for Single Conjugate Adaptive Optics

    • Jenny Niebsch, Ronny Ramlau

    Pages 303-322

13. Inverse Problems of Single Molecule Localization Microscopy

    • Montse Lopez-Martinez, Gwenael Mercier, Kamran Sadiq, Otmar Scherzer, Magdalena Schneider, John C. Schotland et al.

    Pages 323-376

14. Parameter Identification for the Landau–Lifshitz–Gilbert Equation in Magnetic Particle Imaging

    • Barbara Kaltenbacher, Tram Thi Ngoc Nguyen, Anne Wald, Thomas Schuster

    Pages 377-412

15. An Inverse Source Problem Related to Acoustic Nonlinearity Parameter Imaging

    • Masahiro Yamamoto, Barbara Kaltenbacher

    Pages 413-456

Inverse problems such as imaging or parameter identification deal with the recovery of unknown quantities from indirect observations, connected via a model describing the underlying context. While traditionally inverse problems are formulated and investigated in a static setting, we observe a significant increase of interest in time-dependence in a growing number of important applications over the last few years. Here, time-dependence affects a) the unknown function to be recovered and / or b) the observed data and / or c) the underlying process. Challenging applications in the field of imaging and parameter identification are techniques such as photoacoustic tomography, elastography, dynamic computerized or emission tomography, dynamic magnetic resonance imaging, super-resolution in image sequences and videos, health monitoring of elastic structures, optical flow problems or magnetic particle imaging to name only a few. Such problems demand for innovation concerning their mathematical description and analysis as well as computational approaches for their solution.

• Dynamic inverse problem
• imaging
• parameter identification
• regularization methods
• dynamic tomography
• dynamic magnetic resonance
• evolution equations
• elasticity
• viscoelasticity
• magnetic particle imaging
• emission tomography
• motion compensation
• wave equation
• velocity estimation
• movement manipulation

• Department of Mathematics, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria

  Barbara Kaltenbacher

• Department of Mathematics, Saarland University, Saarbrücken, Germany

  Thomas Schuster, Anne Wald

Barbara Kaltenbacher has received her PhD (1996) and her Habilitation (2003) in mathematics at the University of Linz. After professor positions for optimization at the University of Stuttgart and for applied mathematics at the University of Graz, she is professor of Applied Analysis at the University of Klagenfurt since 2011. Her reseach interests lie in the field of inverse problems, in particular regularization methods and parameter identification in partial differential equations, as well as in modeling, for example in nonlinear acoustics and piezoelectricity. She has co-authored tree research monographs and published more than 100 refereed journal and proceedings papers. This work has been supported by the Austrian and the German Science Foundations, as well as by industrial partners in a number of projects. She currently serves as an editorial board member for Inverse Problems and the IMA Journal of Numerical Analysis as well as an editor in chief of the Journal of theEuropean Mathematical Society.


Thomas Schuster studied mathematics and computer science at Saarland University in Saarbrücken where he also got his PhD (1999) and Habilitation (2004). After positions as a Visiting Assistant Professor at Tufts University Medford, MA, USA, as an Associate Professor for Applied Mathematics at Helmut Schmidt University Hamburg, as a Full Professor for Numerical Mathematics in Oldenburg he holds since 2012 a Chair as Full Professor for Numerical Mathematics at Saarland University in Saarbrücken. His research are theoretical foundations and applications for inverse and ill-posed problems. Besides the extension of regularization theory from classical settings to Banach spaces, he currently investigates the application of concepts from machine learning to the solution of inverse problems. The applications of his research range from computerized and terahertz tomography, vector and tensor field tomography, to magnetic particle imaging and damage detection in elastic materials. He co-authored three monographs and published more than 60 journal and proceeding articles. His research was supported by the German Science Foundation, the Federal Ministry of Education and Research, the Federal Ministry for Economic Affairs and Energy, and industrial partners. Currently he acts as an Editorial Board Member of Inverse Problems and Mathematical Problems in Engineering.


Anne Wald studied mathematics and physics at Saarland University in Saarbrücken, Germany. She received her master’s degree in mathematics in 2012 and her diploma in physics in 2013. In 2017, she finished her Ph.D., also at Saarland University, where she currently works as a senior researcher. In her research, she mainly focuses on inverse problems in medicine and engineering, particularly on modeling aspects, mathematical analysis as well as fast and stable solution techniques. Applications include terahertz tomography, magnetic particleimaging, computerized tomography, and parameter identification for the monitoring of material structure. Her research is partly funded by the German Ministry of Education and Research.

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