The Radon Transform - Theory and Implementation
The Radon Transform - Theory and Implementation
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发表时间：
1996-11
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通讯作者：
P. Toft
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作者：
P. Toft
本博士论文的主题是数学 Radon 变换，它非常适合数字图像中的曲线检测和断层扫描图像的重建。论文分为两个主要部分，第一部分描述了 Radon 和 Hough 变换，特别是它们在数字图像中曲线参数检测方面的离散近似。从数字信号处理的角度回顾了 Radon 变换的采样关系。研究了离散 Radon 变换的曲线检测以及假设涵盖各种类型的噪声时有关 Radon 变换性能的方面。此外提出了一种新的估计曲线参数的快速方案。论文的第二部分描述了 D 和 D 中的逆氡变换，重点是断层扫描图像的重建。分析了一些直接重建方案，包括它们的离散实现。此外，回顾了几种基于线性代数的迭代重建方案，并将其应用于正电子发射断层扫描 PET 图像的重建。设计了一种新的、非常快速的迭代重建方法的实现。在更实用的章节中，对 PET 图像中的噪声进行了建模。来自大量测量已经开发并免费提供了几个基于 Radon 和 Hough 变换的曲线检测以及直接迭代 D 和 D 重建的软件包
The subject of this Ph D thesis is the mathematical Radon transform which is well suited for curve detection in digital images and for reconstruction of tomography images The thesis is divided into two main parts Part I describes the Radon and the Hough transform and especially their discrete approxim ations with respect to curve parameter detection in digital images The sampling relationships of the Radon transform is reviewed from a digital signal processing point of view The discrete Radon transform is investigated for detection of curves and aspects regarding the performance of the Radon transform assuming various types of noise is covered Furthermore a new fast scheme for estimating curve parameters is presented Part II of the thesis describes the inverse Radon transform in D and D with focus on re construction of tomography images Some of the direct reconstruction schemes are analyzed including their discrete implementation Furthermore several iterative reconstruction schemes based on linear algebra are reviewed and applied for reconstruction of Positron Emission Tomo graphy PET images A new and very fast implementation of D iterative reconstruction methods is devised In a more practical oriented chapter the noise in PET images is modelled from a very large number of measurements Several packages for Radon and Hough transform based curve detection and direct iterative D and D reconstruction have been developed and provided for free