Table of Contents
CT & Mathematics
Outline
A Little Bit History
Exponential Attenuation of X-ray
Ray-Sum of X-ray Attenuation
Completeness Condition
First Generation
Third Generation
Projection & Sinogram
Computed Tomography
Spiral CT Scanner
Radon Transform
Related Transforms
Outline
Heuristics 1: Sum Game
Approach 1: Linear Algebra
Let Us Guess
Linear Blurring Model
Algo 1.1. EM Iterative Deblurring
Why EM Iterative Deblurring?
Algo 1.2. ART Iterative Deblurring
Heuristics 2: Wave Decomposition
Approach 2: Transformation
Fourier Transformation
Fourier Slice Theorem
From Projections to Image
Algo 2.1. Filtered Backprojection
Derivative-Free Fan-Beam Formula
Radon & Fourier Transforms
Backprojection
Unified Inversion Formula
Heuristics 3: Peeling an Onion
Approach 3: Series Expansion
Algo 3.1. Series Expansion
Algo 3.1. Series Expansion
Exterior Problem
Outline
What is Cone-Beam Tomography?
AMIL X-ray Cone-Beam ?CT System
Completeness Condition: Cone-Beam
From Cone-Beam to Radon Data
Generalized Feldkamp Algorithm
Real Cone-Beam Reconstruction
What is Real-Time Tomography?
Row-Action EM Deblurring
Speed Improvement
Simulation - RAEM for MAR
Simulation - RAEM for Denoising
CT Phantom Test - RAEM
Further Readings
Acknowledgments
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