Comparison of four natural pixel bases for SPECT imaging

In this paper the problem of restoring a two-dimensional tomographic medical image is considered. The emission function f ( P ) is defined on a plane circular domain Ω , and has to be restored from data collected by a SPECT machine. Through an approach known as natural pixel discretization, the solu...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 198; no. 2; pp. 361 - 377
Main Authors: Bevilacqua, R., Bozzo, E., Menchi, O.
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 15.01.2007
Elsevier
Subjects:
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Exact sciences and technology
Fourier analysis
Ill-posedness
Image processing
Information, signal and communications theory
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Pattern recognition. Digital image processing. Computational geometry
Regularization
Restoration
Sciences and techniques of general use
Signal processing
Telecommunications and information theory
Image processing
Restoration
Regularization
Ill-posedness
Fast Fourier transformation
Numerical linear algebra
Image restoration
Discretization method
Direct method
Numerical analysis
Linear system
Matrix inversion
Applied mathematics
Imaging
Two-dimensional calculations
Ill posed problem
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:In this paper the problem of restoring a two-dimensional tomographic medical image is considered. The emission function f ( P ) is defined on a plane circular domain Ω , and has to be restored from data collected by a SPECT machine. Through an approach known as natural pixel discretization, the solution is expressed as a linear combination of functions belonging to a suitable basis. We consider here four different bases, all of them giving a highly structured coefficient matrix. The linear system obtained in this way can be solved efficiently by means of the fast Fourier transform. The computational cost and the performance of the bases are compared. When the data are contaminated by Poissonian noise, the numerical experimentation shows that all the bases are almost equivalent from the point of view of the restoration efficiency. Hence the choice of a basis should rely on other considerations, as for instance the computational cost.
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.07.027