Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography-Type Projection Data
VSP International Science Publishers (Verlag)
978-90-6764-332-0 (ISBN)
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The first part of this new volume in the Inverse and Ill-Posed Problems Series studies uniqeness questions for recovering the shapes of the convex and more complicated bodies from shapes of their projections onto planes of low dimension. Some stability estimates of the solutions to these inverse problems are given.
The second part deals with inverse problems with projection data directly connected to tomography, in partcular to apparent contours of smooth surfaces, which have practical interpretations such as thin cracks in continuous media which are studied in industrial defectoscopy, caustic surfaces which are studies in wave optics, etc.
New results on reconstruction of smooth surfaces from observations of the wave fronts generated by these surfaces are obtained.
CHAPTER 1. INTRODUCTION
Notation and basic definitions
Translation equivalence of projections. Preliminary results
CHAPTER 2. SO(2)-CONGRUENCE OF PROJECTIONS
The case of convex bodies
An attempt to relax the asymmetry conditions
The case of ( n - 2)-visible and ( n - 2)-convex bodies
Stability estimates for recovering the shapes of convex bodies from the shapes of their projections
CHAPTER 3. OTHER GROUPS OF CONGRUENCES OF PROJECTIONS
SO(2)-similarity of projections
SO(3)-congruence of projections
SU(2) and U-congruence of projections
CHAPTER 4. APPARENT CONTOURS AND OTHER TOMOGRAPHY-TYPE PROJECTION DATA
Reconstruction of surfaces from the shapes of their apparent contours and the stationary phase observations
Inversion formulae for integral geometry problems and an algorithm of computerized tomography
An inverse problem for the Hamilton-Jacobi equations
Inverse problems for one class of the tomography-type evolution equation
Bibliography
| Erscheint lt. Verlag | 28.11.2000 |
|---|---|
| Reihe/Serie | Inverse and Ill-Posed Problems Series |
| Verlagsort | Zeist |
| Sprache | englisch |
| Gewicht | 385 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| ISBN-10 | 90-6764-332-7 / 9067643327 |
| ISBN-13 | 978-90-6764-332-0 / 9789067643320 |
| Zustand | Neuware |
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