23-06-2012, 10:57 AM
Overview of Methods for Image Reconstruction From Projections in Emission Computed Tomography
[attachment=25177]
INTRODUCTION
Emission computed tomography (ECT) is a technology
for medical imaging whose importance is increasing rapidly.
There is a growing appreciation of the significance of the
functional (as opposed to anatomical) information that
is provided by ECT, and of its value for the purposes of
medical diagnosis and monitoring the response to therapy.
PROBLEM FORMULATION FOR EMISSION TOMOGRAPHY
Many applications where indirect imaging is employed,
including ECT, involve discrete measurements that correspond
to some integral transformation of a function of continuous
spatial variables, where the function and the image to
be reconstructed from the data both represent the spatial distribution
of some physical property of interest inside the object
being imaged. In these applications, the process of data
collection is naturally represented by a discrete-continuous
(D-C) model that relates the discrete data to the function of
continuous spatial variables.
IMAGE RECONSTRUCTION APPROACH BASED ON D-C
MODEL
This approach leads to a direct solution to the fundamental
D-C problem without introducing further discretization or
approximation. Although the approach has this attractive theoretical
property, the methods based on it are not widely used
in PET or SPECT, so our description of this approach is more
brief than that of the other approaches.
CONCLUSION
This paper has used the various models of the data collection
process as the framework for presenting an overview
of the wide variety of methods that have been developed for
image reconstruction in PET and SPECT. The overall sequence
of the major sections in the paper, and the presentation
within each major section, both proceed from the more
realistic and general models to those that are idealized and
application-specific. For most of the topics, the description
proceeds from the 3-D case to the 2-D case.
[attachment=25177]
INTRODUCTION
Emission computed tomography (ECT) is a technology
for medical imaging whose importance is increasing rapidly.
There is a growing appreciation of the significance of the
functional (as opposed to anatomical) information that
is provided by ECT, and of its value for the purposes of
medical diagnosis and monitoring the response to therapy.
PROBLEM FORMULATION FOR EMISSION TOMOGRAPHY
Many applications where indirect imaging is employed,
including ECT, involve discrete measurements that correspond
to some integral transformation of a function of continuous
spatial variables, where the function and the image to
be reconstructed from the data both represent the spatial distribution
of some physical property of interest inside the object
being imaged. In these applications, the process of data
collection is naturally represented by a discrete-continuous
(D-C) model that relates the discrete data to the function of
continuous spatial variables.
IMAGE RECONSTRUCTION APPROACH BASED ON D-C
MODEL
This approach leads to a direct solution to the fundamental
D-C problem without introducing further discretization or
approximation. Although the approach has this attractive theoretical
property, the methods based on it are not widely used
in PET or SPECT, so our description of this approach is more
brief than that of the other approaches.
CONCLUSION
This paper has used the various models of the data collection
process as the framework for presenting an overview
of the wide variety of methods that have been developed for
image reconstruction in PET and SPECT. The overall sequence
of the major sections in the paper, and the presentation
within each major section, both proceed from the more
realistic and general models to those that are idealized and
application-specific. For most of the topics, the description
proceeds from the 3-D case to the 2-D case.