Radon Transform
Radon Transform and Inversion
Range Conditions and Frequency Analysis
Support Theorem
Reconstruction of Functions from Attenuated Integrals
Reconstruction of Differential Forms
Ray and Line Integral Transforms
Introduction
Reconstruction from Line Integrals
Range Conditions
Shift-Invariant FBP Reconstruction
Backprojection Filtration Method
Tuy’s Regularized Method
Ray Integrals of Differential Forms
Symmetric Tensors and Differentials
Reconstruction from Ray Integrals
Factorization Method
Factorable Maps
Spaces of Constant Curvature
Funk Transform on the Orthogonal Group
Reconstruction from Non-Redundant Data
Range Conditions
General Method of Reconstruction
Geometric Integral Transforms
Reconstruction
Integral Transforms with Weights
Resolved Generating Functions
Analysis of Convergence
Wave Front of Integral Transform
Applications to Classical Geometries
Minkowski–Funk Transform
Nongeodesic Hyperplane Sections of a Sphere
Totally Geodesic Transform in Hyperbolic Spaces
Horospherical Transform
Hyperboloids
Cormack’s Curves
Confocal Paraboloids
Cassini Ovals and Ovaloids
Applications to the Spherical Mean Transform
Oscillatory Sets
Reconstruction
Examples
Time Reversal Structure
Boundary Isometry for Waves in a Cavity
Range Conditions
Spheres Tangent to a Hyperplane
Summary of Spherical Mean Transform
Appendix
Bibliographic notes appear at the end of each chapter.
Biography
Victor Palamodov is a professor in the School of Mathematical Sciences at Tel-Aviv University. His research interests include mathematical and algebraic analysis and applications to physics and medical diagnostics.
