1 Generalized Radon transforms
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Sean Holman
Abstract
Generalized Radon transforms (GRTs) integrate a function over a family of possibly curved surfaces, and the need for their inversion arises in many applications including ultrasound, seismic imaging, synthetic aperture radar (SAR), thermoacoustic and photoacoustic tomography, emission tomography, Compton scattering tomography and Compton camera imaging among others. This paper introduces GRTs and their basic properties, and then surveys some of the applications mentioned, microlocal analysis of GRTs and explicit inversion formulae for GRTs.
Abstract
Generalized Radon transforms (GRTs) integrate a function over a family of possibly curved surfaces, and the need for their inversion arises in many applications including ultrasound, seismic imaging, synthetic aperture radar (SAR), thermoacoustic and photoacoustic tomography, emission tomography, Compton scattering tomography and Compton camera imaging among others. This paper introduces GRTs and their basic properties, and then surveys some of the applications mentioned, microlocal analysis of GRTs and explicit inversion formulae for GRTs.
Kapitel in diesem Buch
- 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
Kapitel in diesem Buch
- 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
