Imaging, Multi-scale and High Contrast Partial Differential Equations
About this Title
Habib Ammari, Ecole Normale Supérieure, Paris, France, Yves Capdeboscq, Mathematical Institute, Oxford, United Kingdom, Hyeonbae Kang, Inha University, Incheon, Korea and Imbo Sim, National Institute of Mathematical Sciences, Daejeon, Korea, Editors
Publication: Contemporary Mathematics
Publication Year 2016: Volume 660
ISBNs: 978-1-4704-1923-3 (print); 978-1-4704-2932-4 (online)
This volume contains the proceedings of the Seoul ICM 2014 Satellite Conference on Imaging, Multi-scale and High-Contrast PDEs, held from August 7–9, 2014, in Daejeon, Korea.
The mathematical analysis of partial differential equations modelling materials, or tissues, presenting multiple scales has been a very active area of research. The study of the corresponding imaging or reconstruction problem is a more recent area. If the material parameters of the partial differential equation present high contrast ratio, then the solution to the PDE becomes particularly challenging to analyze and compute. On the other hand, imaging in highly heterogeneous media poses significant challenges to the mathematical community.
The focus of this volume is on recent progress towards complete understanding of the direct problem with high contrast or high frequencies, and unified approaches to the inverse and imaging problems for both small and large contrast or frequencies. Of particular importance in imaging are shape representation techniques and regularization approaches. Special attention is devoted to new models and problems coming from physics leading to innovative imaging and signal processing methods.
Graduate students and research mathematicians interested in applied math, inverse problems, and imaging PDEs.
Table of Contents
- Habib Ammari, Stéphane Mallat, Irène Waldspurger and Han Wang – Wavelet methods for shape perception in electro-sensing
- Habib Ammari and Han Wang – Time-domain multiscale shape identification in electro-sensing
- Hyeonbae Kang and Eunjoo Kim – Estimation of stress in the presence of closely located elastic inclusions: A numerical study
- Hyundae Lee and Jaeyoung Lee – Array dependence of effective parameters of dilute periodic elastic composite
- Mikyoung Lim – A review on the enhancement of near-cloaking using the multilayer structure
- Giovanni S. Alberti and Yves Capdeboscq – On local non-zero constraints in PDE with analytic coefficients
- Josselin Garnier – Daylight imaging for virtual reflection seismology
- Muhammad Afzal, Muhammad Ayub, Rab Nawaz and Abdul Wahab – Mode-matching solution of a scattering problem in flexible waveguide with abrupt geometric changes
- Durga Prasad Challa – Direct scattering by a sound hard small body
- Giulio Ciraolo – Helmholtz equation in unbounded domains: Some convergence results for a constrained optimization problem