**Contemporary Mathematics**

Volume: 660;
2016;
148 pp;
Softcover

MSC: Primary 35; 65; 86;

Print ISBN: 978-1-4704-1923-3

Product Code: CONM/660

List Price: $108.00

Individual Member Price: $86.40

**Electronic ISBN: 978-1-4704-2932-4
Product Code: CONM/660.E**

List Price: $108.00

Individual Member Price: $86.40

# Imaging, Multi-scale and High Contrast Partial Differential Equations

Share this page *Edited by *
*Habib Ammari; Yves Capdeboscq; Hyeonbae Kang; Imbo Sim*

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.

#### Readership

Graduate students and research mathematicians interested in applied math, inverse problems, and imaging PDEs.

# Table of Contents

## Imaging, Multi-scale and High Contrast Partial Differential Equations

- Cover Cover11
- Title page i4
- Contents v6
- Preface vii8
- Wavelet methods for shape perception in electro-sensing 110
- 1. Introduction 110
- 2. Modelling of the electro-sensing problem 211
- 3. Polynomial basis and linear estimation 918
- 4. Wavelet basis and nonlinear estimation 1019
- 5. Numerical experiments 1423
- 6. Discussion 1524
- 7. Conclusion 1726
- Appendix A. Proof of Lemma 2.2 1827
- Appendix B. Proof of Proposition 2.4 1827
- Appendix C. Proof of Proposition 4.1 1928
- References 1928

- Time-domain multiscale shape identification in electro-sensing 2332
- 1. Introduction 2332
- 2. Electro-sensing model 2534
- 3. Representation of solution 2736
- 4. Time-dependent GPTs and asymptotic expansions 3140
- 5. Shape identification with pulse-type signals 3544
- 6. Numerical Experiments 3746
- 7. Discussion and conclusion 4150
- Appendix A. Numerical solution of the forward problem 4251
- References 4251

- Estimation of stress in the presence of closely located elastic inclusions: A numerical study 4554
- Array dependence of effective parameters of dilute periodic elastic composite 5968
- A review on the enhancement of near-cloaking using the multilayer structure 7382
- On local non-zero constraints in PDE with analytic coefficients 8998
- Daylight imaging for virtual reflection seismology 99108
- Mode-matching solution of a scattering problem in flexible waveguide with abrupt geometric changes 113122
- Direct scattering by a sound hard small body 131140
- Helmholtz equation in unbounded domains: Some convergence results for a constrained optimization problem 139148
- Back Cover Back Cover1160