Analytical inversion formula for uniformly attenuated fan-beam projections

Author

Weng, Yi ; Zeng, Gengsheng L. ; Gullberg, Grant T.

Author_Institution

Dept. of Radiol., Utah Univ., Salt Lake City, UT, USA

Volume

44

Issue

2

fYear

1997

fDate

4/1/1997 12:00:00 AM

Firstpage

243

Lastpage

249

Abstract

A convolution backprojection algorithm was derived by Tretiak and Metz (198) to reconstruct two-dimensional (2-D) transaxial slices from uniformly attenuated parallel-beam projections. Using transformation of coordinates, this algorithm can be modified to obtain a formulation useful to reconstruct uniformly attenuated fan-beam projections. Unlike that for parallel-beam projections, this formulation does not produce a filtered backprojection reconstruction algorithm but instead has a formulation that is an inverse integral operator with a spatially varying kernel. This algorithm thus requires more computation time than does the filtered backprojection reconstruction algorithm for the uniformly attenuated parallel-beam case. However, the fan-beam reconstructions demonstrate the same image quality as that of parallel-beam reconstructions

Keywords

image reconstruction; inverse problems; medical image processing; single photon emission computed tomography; SPECT; analytical inversion formula; computation time; convolution backprojection algorithm; image quality; inverse integral operator; parallel-beam reconstructions; spatially varying kernel; two-dimensional transaxial slice reconstruction; uniformly attenuated fan-beam projections; Algorithm design and analysis; Attenuation; Convolution; Geometry; Image reconstruction; Iterative algorithms; Kernel; Reconstruction algorithms; Single photon emission computed tomography; Two dimensional displays;

fLanguage

English

Journal_Title

Nuclear Science, IEEE Transactions on

Publisher

ieee

ISSN

0018-9499

Type

jour

DOI

10.1109/23.568816

Filename

568816