An SVD reconstruction algorithm using a natural pixel representation of the attenuated Radon transform

Author

Gullberg, Grant T. ; Hsieh, Yu-Lung ; Zeng, GI Larry

Author_Institution

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

Volume

43

Issue

1

fYear

1996

fDate

2/1/1996 12:00:00 AM

Firstpage

295

Lastpage

303

Abstract

The purpose of this work was to investigate the use of natural pixels to reconstruct attenuation corrected emission data using attenuation factors calculated from a natural pixel representation of the reconstructed transmission data. The reconstruction algorithm for both transmission and emission reconstructions is based on the assumption that a continuous image can be obtained by backprojecting the discrete array q, which is the least squares solution to Mq=p, where p is the array of discrete measurements. The M matrix represents the operator obtained from the backprojection operator followed by the projection operator using the natural pixel basis. A singular value decomposition was used to solve the equation Mq=p, and the final image was obtained by sampling the continuous backprojection of the solution q at a discrete array of points. Computer simulations showed that accurate attenuation corrected reconstructions could be obtained using a natural pixel representation of the attenuated Radon transform for a variable attenuator

Keywords

Radon transforms; emission tomography; image reconstruction; medical image processing; singular value decomposition; SVD reconstruction algorithm; attenuated Radon transform; attenuation corrected emission data; computer simulations; continuous backprojection; discrete array backprojection; least squares solution; medical diagnostic imaging; natural pixel representation; nuclear medicine; projection operator; variable attenuator; Attenuation; Computer simulation; Equations; Image reconstruction; Image sampling; Least squares methods; Matrix decomposition; Q measurement; Reconstruction algorithms; Singular value decomposition;

fLanguage

English

Journal_Title

Nuclear Science, IEEE Transactions on

Publisher

ieee

ISSN

0018-9499

Type

jour

DOI

10.1109/23.485969

Filename

485969