**Contemporary Mathematics**

Volume: 615;
2014;
309 pp;
Softcover

MSC: Primary 35;

**Print ISBN: 978-1-4704-1079-7
Product Code: CONM/615**

List Price: $109.00

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MAA Member Price: $98.10

**Electronic ISBN: 978-1-4704-1659-1
Product Code: CONM/615.E**

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# Inverse Problems and Applications

Share this page *Edited by *
*Plamen Stefanov; András Vasy; Maciej Zworski*

This volume contains the proceedings of two
conferences on Inverse Problems and Applications, held in 2012, to
celebrate the work of Gunther Uhlmann. The first conference was held
at the University of California, Irvine, from June 18–22, 2012, and
the second was held at Zhejiang University, Hangzhou, China, from
September 17–21, 2012.

The topics covered include inverse problems in medical imaging,
scattering theory, geometry and image processing, and the mathematical
theory of cloaking, as well as methods related to inverse problems.

#### Readership

Graduate students and research mathematicians interested in applied analysis, inverse problems, mathematical theory of cloaking, and medical imaging.

# Table of Contents

## Inverse Problems and Applications

- Preface vii8 free
- Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking by anomalous localized resonance II 110 free
- Hybrid inverse problems and redundant systems of partial differential equations 1524
- A Direct Imaging Method for Inverse Scattering Using the Generalized Foldy–Lax Formulation 4958
- The Inverse Scattering Problem for a Penetrable Cavity with Internal Measurements 7180
- A Neumann series based method for photoacoustic tomography on irregular domains 8998
- Nonlinear Inversion from Partial EIT Data:Computational Experiments 105114
- 1. Introduction 105114
- 2. Method 1: The method based on the Schrödinger equation 111120
- 3. Method 2: The method based on a ∂_{𝑧} and \overline{∂}_{𝑧} system 112121
- 4. Computation of Partial Boundary Data CGO Solutions 113122
- 5. Numerical Reconstruction of Conductivities from Partial Data Using Method 2 117126
- 6. Computational Experiments 119128
- 7. Conclusions 122131
- Acknowledgments 127136
- References 127136

- Increasing stability of the inverse boundary value problem for the Schrödinger equation 131140
- Recent progress of inverse scattering theory on non-compact manifolds 143152
- On an inverse problem for the Steklov spectrum of a Riemannian surface 165174
- 1. Introduction 165174
- 2. The problem of determining a metric on the disc 167176
- 3. The problem of determining a positive function on the circle 169178
- 4. The problem of recovering a planar domain 176185
- 5. Two classes of Riemannian metrics 178187
- 6. A scalar Riemann –Hilbert problem 182191
- Appendix A. Proofs of Theorems 5.1 and 5.2 and of Lemma 6.2 188197
- References 190199

- Recent progress in the Calderón problem with partial data 193202
- Local reconstruction of a Riemannian manifold from a restriction of the hyperbolic Dirichlet-to-Neumann operator 223232
- Damping Mechanisms for Regularized Transformation-acoustics Cloaking 233242
- Hybrid Inverse Problem for Porous Media 255264
- Efficient Algorithms for Ptychographic Phase Retrieval 261270
- Matrix elements of Fourier Integral Operator 281290