Biomedical Engineering Reference
In-Depth Information
Chapter3
PETImageReconstruction
Frank Wubbeling
Department of Mathematics and Computer Science, University of Munster,
Munster, Germany
3.1
Introduction ::::::::::::::::::::::::::::::::::::::::::::::::::::::
31
3.2
Analytical algorithms ::::::::::::::::::::::::::::::::::::::::::::
32
3.2.1
Mathematical basis ::::::::::::::::::::::::::::::::::::::
32
3.2.2
Filtered backprojection ::::::::::::::::::::::::::::::::::
35
3.2.3
Implementation: Resolution and complexity ::::::::::::
37
3.2.4
Implementation and rebinning ::::::::::::::::::::::::::
38
3.2.4.1
2D Rebinning :::::::::::::::::::::::::::::::::
39
3.2.4.2
3D ltered backprojection ::::::::::::::::::::
40
3.2.5
Limitations ::::::::::::::::::::::::::::::::::::::::::::::
40
3.3
Discrete algorithms ::::::::::::::::::::::::::::::::::::::::::::::
40
3.3.1
ART|Algebraic reconstruction technique ::::::::::::::
41
3.3.2
EM :::::::::::::::::::::::::::::::::::::::::::::::::::::::
42
3.3.3
Computing the system matrix :::::::::::::::::::::::::::
44
3.3.4
List mode ::::::::::::::::::::::::::::::::::::::::::::::::
45
3.4
Summary :::::::::::::::::::::::::::::::::::::::::::::::::::::::::
47
References :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
47
3.1 Introduction
In this chapter, we give a short review of image reconstruction algorithms
for positron emission tomography. The basic problem is: How do we convert
the measurements of counts on a set of lines of response into a plot of the
activity function f of a radioactive agent?
Basically, we distinguish two types of algorithms: analytical algorithms
based on a mathematical analysis of the Radon transform, usually employing
the filtered backprojection, and numerical algorithms based on a discretization
of the problem, usually employing the expectation-maximization algorithm or
one of its variants. While the former one is very fast and mathematically
rigorous in two dimensions, it does not have an obvious extension to 3D,
nor can it easily handle deviations to the Radon transform such as scatter,
31
 
 
 
Search WWH ::




Custom Search