4 Inverse problems in cosmological X-ray tomography
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Yiran Wang
Abstract
We consider the recovery of space-time structures from the Cosmic Microwave Background (CMB) using tomography methods. On the linearization level, the problem concerns an X-ray transform in Lorentzian geometry, called the light ray transform. We review recent results on the mathematical properties of the transform, and their applications to the CMB inverse problem for various physical models.
Abstract
We consider the recovery of space-time structures from the Cosmic Microwave Background (CMB) using tomography methods. On the linearization level, the problem concerns an X-ray transform in Lorentzian geometry, called the light ray transform. We review recent results on the mathematical properties of the transform, and their applications to the CMB inverse problem for various physical models.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- 1 Generalized Radon transforms 1
- 2 Nonstandard Sobolev scales and the mapping properties of the X-ray transform on manifolds with strictly convex boundary 35
- 3 On geometric inverse problems and microlocal analysis 77
- 4 Inverse problems in cosmological X-ray tomography 139
- 5 The weighted X-ray transform and applications 167
- Index 187
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- 1 Generalized Radon transforms 1
- 2 Nonstandard Sobolev scales and the mapping properties of the X-ray transform on manifolds with strictly convex boundary 35
- 3 On geometric inverse problems and microlocal analysis 77
- 4 Inverse problems in cosmological X-ray tomography 139
- 5 The weighted X-ray transform and applications 167
- Index 187
