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This proceedings volume gathers peer-reviewed, selected papers presented at the "Mathematical and Numerical Approaches for Multi-Wave Inverse Problems" conference at the Centre Internacional de Rencontres Mathématiques (CIRM) in Marseille, France, in April 2019. It brings the latest research into new, reliable theoretical approaches and numerical techniques for solving nonlinear and inverse problems arising in multi-wave and hybrid systems.
Multi-wave inverse problems have a wide range of applications in acoustics, electromagnetics, optics, medical imaging, and geophysics, to name but a few. In turn, it is well known that inverse problems are both nonlinear and ill-posed: two factors that pose major challenges for the development of new numerical methods for solving these problems, which are discussed in detail.
These papers will be of interest to all researchers and graduate students working in the fields of nonlinear and inverse problems and its applications.
List of contents
Thermoacoustic Applications (Patch et al.).- On the Transport Method for Hybrid Inverse Problems (Chung et al.).- Stable Determination of an Inclusion in a Layered Medium with Special Anisotropy (Di Cristo).- Convergence of stabilized P1 finite element scheme for time harmonic Maxwell's equations (Asadzadeh et al.).- Regularized Linear Inversion with Randomized Singular Value Decomposition (Ito et al.).- Parameter selection in dynamic contrast-enhanced magnetic resonance tomography (Niinimaki et al.).- Convergence of explicit P1 finite-element solutions to Maxwell's equations (Beilina et al.).- Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography (Elbau et al.).- The finite element method and balancing principle for magnetic resonance imaging (Beilina et al.).
About the author
Larisa Beilina is a Professor of Applied Mathematics at the University of Gothenburg, Sweden. She holds a PhD in Mathematics (2003) from Chalmers University of Technology, and has co-authored and co-edited several books on inverse problems and related fields, including "Inverse Problems and Applications" (ISBN 978-3-319-12498-8), published by Springer. Her main research achievements are in the solution of coefficient inverse problems using an adaptive finite element method for wave propagation and electromagnetics.
Maïtine Bergounioux is an Emeritus Professor at the University of Orléans, France. She holds a PhD in Applied Mathematics (1985) from the University of Lille, France, and the title of Habilitation (1993) from the University of Orléans. She has authored and edited several books, including "Introduction au traitement mathématique des images - méthodes deterministes" (ISBN 978-3-662-46538-7) and "Mathematical Image Processing" (ISBN 978-3-642-19603-4), both published with Springer.
Michel Cristofol is a Professor at Aix-Marseille University, France. He completed his PhD in Mathematics (1998) at the University of Provence, France and his Habilitation (2011) at Aix-Marseille University. His research interests include partial differential equations, inverse problems on hybrid media, and linear and non-linear parabolic systems.
Anabela Da Silva is a CNRS researcher at the Institut Fresnel, France. She holds a PhD in Optics and Photonics (2001) from the University Pierre et Maris Curie, Paris, France, and the title of Habilitation (2013) from Aix-Marseille University, France. Her research interests include the development of optical-based and hybrid biomedical imaging systems, modeling of light propagation through biological tissues with the Radiative Transport Equation, multiphysics modeling, and associated inverse problem resolution methods.
Amelie Litman is a CNRS researcher at the Institut Fresnel, France. She holds a PhD in Applied Mathematics (1997) from the University of Paris Sud, France, and the title of Habilitation (2009) from the University of Provence, France. Her research interests include inverse problems, nonlinear optimization algorithms and electromagnetic scattering.
