Mathematical problems of computerized tomography

The data measured in computerized tomography; e.g., the X-ray attenuation in X-ray tomography or the resonance phenomena in nuclear magnetic resonance tomography, have to be processed to produce the pictures on which the diagnostic evaluation of the physician is based. This process consists of the s...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the IEEE 1983-01, Vol.71 (3), p.379-389
Main Authors: Louis, A.K., Natterer, F.
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
Attenuation measurement
Computed tomography
Computer errors
Computer science
control theory
systems
Exact sciences and technology
Instruments
Nuclear magnetic resonance
Nuclear measurements
Pattern recognition. Digital image processing. Computational geometry
Size measurement
Stability
X-ray tomography
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The data measured in computerized tomography; e.g., the X-ray attenuation in X-ray tomography or the resonance phenomena in nuclear magnetic resonance tomography, have to be processed to produce the pictures on which the diagnostic evaluation of the physician is based. This process consists of the solution of the following mathematical problem. The data depend on the searched-for distribution and this dependence can be described as an integral transform. To produce the final picture amounts to the inversion of the integral transform. This paper is concerned with the description of the integral transforms modeling the different techniques in computerized tomography. Among other things, the following questions are treated. Which numerical problems do we have to encounter in inverting the transforms; e.g., what accuracy in the reconstruction can we expect in dependence on the accuracy of the data. To what extent is a distribution determined by a finite number of measurements. Is it possible to recover the distribution reliably if the data are incomplete.
ISSN:0018-9219
1558-2256
DOI:10.1109/PROC.1983.12596