The Radon Transform and Local Tomography [Hardcover]

Over the past decade, the field of image processing has made tremendous advances. One type of image processing that is currently of particular interest is tomographic imaging, a technique for computing the density function of a body, or discontinuity surfaces of this function. Today, tomography is widely used, and has applications in such fields as medicine, engineering, physics, geophysics, and security. The Radon Transform and Local Tomography clearly explains the theoretical, computational, and practical aspects of applied tomography. It includes sufficient background information to make it essentially self-contained for most readers.Introduction
Brief Description of New Results and the Aims of the Book
Review of Some Applications of the Radon Transform
Properties of the Radon Transform and Inversion Formulas
Definitions and Properties of the Radon Transform and Related Transforms
Inversion Formulas for R
Singular Value Decomposition of the Radon Transform
Estimates in Sobolev Spaces
Inversion Formulas for the Backprojection Operator
Inversion Formulas for X-Ray Transform
Uniqueness Theorems for the Radon and X-Ray Transforms
Attenuated and Exponential Radon Transforms
Convergence Properties of the Inversion Formulas on Various Classes of Functions
Range Theorems and Reconstruction Algorithms
Range Functions for R on Smooth Functions
Range Functions for R on Sobolev Spaces
Range Theorems for R*
Range Theorem for X-Ray Transform
Numerical Solution of the Equation Rf = g with Noisy Data
Filtered Backprojection Algorithm
Other Reconstruction Algorithms
Singularities of the Radon Transform
Introduction
Singular Support of the Radon Transform
The Relation Between S and S (WE NEED A HAT OVER THE LAST S. See hard copy of toc for details)
The Envelopes and the Duality Law
Asymptotics of Rf Near S
Singularitil³-