Inverse Problems and Applications: Inside Out II

Mathematical Sciences Research Institute

doi:10.1017/9781139424417

Inverse problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a variety of medical and other imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the Earth's interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modeling in the life sciences among others. The expository survey essays in this book describe recent developments in inverse problems and imaging, including hybrid or couple-physics methods arising in medical imaging, Calderon's problem and electrical impedance tomography, inverse problems arising in global seismology and oil exploration, inverse spectral problems, and the study of asymptotically hyperbolic spaces. It is suitable for graduate students and researchers interested in inverse problems and their applications.

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Contents

Frontmatter
pp i-vi
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Contents
pp vii-viii
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Preface
pp ix-xii
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Calderón’s inverse problem: imaging and invisibility
pp 1-54
- By Kari Astala, Matti Lassas, Lassi Päivärinta
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Resistor network approaches to electrical impedance tomography
pp 55-118
- By Liliana Borcea, Vladimir Druskin, Fernando Guevara Vasquez, Alexander V. Mamonov
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The Calderón inverse problem in two dimensions
pp 119-166
- By Colin Guillarmou, Leo Tzou
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The Calderón problem on Riemannian manifolds
pp 167-248
- By Mikko Salo
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Enclosure methods for Helmholtz-type equations
pp 249-270
- By Jenn-Nan Wang, Ting Zhou
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Multiwave methods via ultrasound
pp 271-324
- By Plamen Stefanov, Gunther Uhlmann
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Hybrid inverse problems and internal functionals
pp 325-368
- By Guillaume Bal
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Inverse problems for connections
pp 369-410
- By Gabriel P. Paternain
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Elastic-wave inverse scattering based on reverse time migration with active and passive source reflection data
pp 411-454
- By Valeriy Brytik, Maarten V. De Hoop, Robert D. Van Der Hilst
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Inverse problems in spectral geometry
pp 455-486
- By Kiril Datchev, Hamid Hezari
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Microlocal analysis of asymptotically hyperbolic spaces and high energy resolvent estimates
pp 487-528
- By András Vasy
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Transmission eigenvalues in inverse scattering theory
pp 529-580
- By Fioralba Cakoni, Houssem Haddar
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Inverse Problems and Applications

Inside Out II

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-xii

Calderón’s inverse problem: imaging and invisibility
pp 1-54

Resistor network approaches to electrical impedance tomography
pp 55-118

The Calderón inverse problem in two dimensions
pp 119-166

The Calderón problem on Riemannian manifolds
pp 167-248

Enclosure methods for Helmholtz-type equations
pp 249-270

Multiwave methods via ultrasound
pp 271-324

Hybrid inverse problems and internal functionals
pp 325-368

Inverse problems for connections
pp 369-410

Elastic-wave inverse scattering based on reverse time migration with active and passive source reflection data
pp 411-454

Inverse problems in spectral geometry
pp 455-486

Microlocal analysis of asymptotically hyperbolic spaces and high energy resolvent estimates
pp 487-528

Transmission eigenvalues in inverse scattering theory
pp 529-580

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Inside Out II

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