Table Of ContentThree-Dimensional Image Reconstruction in
Radiology and Nuclear Medicine
Computational Imaging and Vision
Managing Editor:
MAX A. VIERGEVER.
Utrecht University, Utrecht, The Netherlands
Editorial Board:
OUVIER D. FAUGERAS, INRlA, Sophia-Antipolis, France
JAN J. KOENDERINK, Utrecht University, Utrecht, The Netherlands
STEPHEN M. PIZER, University ofN orth Carolina, Chapel Hill, USA
SABURO TSUn, Osaka University, Osaka, Japan
STEVEN W. ZUCKER, McGill University, Montreal, Canada
Volume 4
Three-Dimensional Image
Reconstruction in Radiology and
Nuclear Medicine
Edited by
Pierre Grangeat
and
lean-Louis Amans
Laboratoire d' Electronique de Technologie et d'Instrumentation,
a
Commissariat l' Energie Atomique, Technologies Avancees,
Grenoble, France
Springer-Science+Business Media, B.Y.
A c.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-4723-6 ISBN 978-94-015-8749-5 (eBook)
DOI 10.1007/978-94-015-8749-5
Printed on acid-free paper
All Rights Reserved
© Springer Science+ Business Media Dordrecht 1996
Originally published by Kluwer Academic Publishers in 1996.
Softcover reprint of the hardcover 1s t edition 1996
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
TABLE OF CONTENTS
PREFACE vii
ACKNOLEDGEMENTS ix
Part 1 : CONE-BEAM AND NEW GEOMETRIES RECONSTRUCTION
Comparison of three 3D reconstruction methods from cone-beam data 3
C. Axelsson-Jacobson, R. Guillemaud, P.-E. Danielsson, P. Grangeat. M Defrise,
R. Clack
Filtered backprojection algorithms for attenuated parallel and cone-beam projections 19
sampled on a sphere
Y. Weng, G.L. Zeng, G. T. Gullberg
A theorem on divergent projections 35
P. R. Edholm, P.-E. Danielsson
An adaptative and constrained model for 3D X-ray vascular reconstruction 47
E. Payot, R. Guillemaud, Y. Trousset, F Preteux
Cone-beam algebraic reconstruction using edge-preserving regularization 59
1. Laurette, P.M Koulibaly, L. Blanc-Feraud, P. Charbonnier, J.c. Nosmas,
M Barlaud, J. Darcourt
Eigen analysis of cone-beam scanning geometries 75
G.L. Zeng, G. T. Gullberg, S.A. Foresti
Efficient sampling in 3D tomography : parallel schemes 87
L. Desbat
Part 2 : SPECT QUANTITATION
Analytical approaches for image reconstruction in 3D SPECT 103
X Pan, c.E. Metz
Quantitative brain SPECT in three dimensions: an analytical approach without 117
transmission scans
Z. Liang, J. Ye, J. Cheng, D. P. Harrington
An analytical approach of compensation for non-uniform attenuation and 3D detector 133
response in cardiac SPECT imaging
S. J. Glick, M A. King, T.-S. Pan, E.J. Soares
vi
Characteristics of reconstructed point response in three-dimensional spatially variant 149
detector response compensation in SPECT
B.MW. Tsui,XD. Zhao, E.C. Frey, z.-w. Ju, G.T. Gullberg
Evaluation offully 3D iterative scatter compensation 163
and post-reconstruction filtering in SPECT
F.J. Beekman, MA. Viergever
An investigation of two approximation methods for improving the speed of 3D iterative 177
reconstruction-based scatter compensation
E.c. Frey, z.-w. Ju, B.MW. Tsui
Part 3: PATIENT MOTION AND GATED SPECT
Evaluation of a 3D OS-EM reconstruction algorithm for correction of patient motion in 197
emission tomography
R.R. Fulton, B.F. Hutton, M Braun, P.K. Hooper, S. Eberl, S.R. Meikle
Space-time Gibbs priors applied to gated SPECT myocardial perfusion studies 209
D.S. Lalush , B. M W. Tsui
Reconstruction of gated SPECT myocardial images 225
images using a temporal evolution model
J. de Murcia, P. Grangeat
Part 4: PET QUANTITATION AND RECONSTRUCTION
Design and performance of 3D single photon transmission measurement on a positron 245
tomograph with continuously rotating detectors
R.A. Dekemp, w.F. Jones, R.S. Beanlands, C. Nahmias
A single scatter simulation technique for scatter correction in 3D PET 255
c.c.
Watson, D. Newport, ME. Casey
The effect of energy threshold on image variance in fully 3D PET 269
J. M Ollinger -
FIPI : fast 3-D PET reconstruction by Fourier inversion of rebinned plane integrals 277
C. Wu, C. E. Ordonez, C. T. Chen
Performance of a fast maximum likelihood algorithm for fully 3D PET reconstruction 297
S. Matel, J. A. Browne
AUTHOR INDEX 317
PREFACE
This book contains a selection of communications presented at the Third International
Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear
Medicine, held 4-6 July 1995 at Domaine d' Aix-Marlioz, Aix-Ies-Bains, France. This
nice resort provided an inspiring environment to hold discussions and presentations on
new and developing issues.
Roentgen discovered X-ray radiation in 1895 and Becquerel found natural radioactivity
in 1896 : a hundred years later, this conference was focused on the applications of such
radiations to explore the human body. If the physics is now fully understood, 3D
imaging techniques based on ionising radiations are still progressing. These techniques
include 3D Radiology, 3D X-ray Computed Tomography (3D-CT), Single Photon
Emission Computed Tomography (SPECT), Positron Emission Tomography (PET).
Radiology is dedicated to morphological imaging, using transmitted radiations from an
external X-ray source, and nuclear medicine to functional imaging, using radiations
emitted from an internal radioactive tracer. In both cases, new 3D tomographic systems
will tend to use 2D detectors in order to improve the radiation detection efficiency.
Taking a set of 2D acquisitions around the patient, 3D acquisitions are obtained. Then,
fully 3D image reconstruction algorithms are required to recover the 3D image of the
body from these projection measurements.
Besides the gain in sensitivity, these fully 3D approaches provide many new
opportunities. For instance, it becomes possible to take into account all the 3D
neighbours of a given local value, and thus to have a better control of the smoothing
effect linked to regularisation constraints, or to have a more precise description of
matter-radiation interactions to compensate for attenuation, scatter or blurring effects.
With 3D acquisitions, we get access to 3D motion compensation linked for instance to
patient displacement. We can also introduce complex 3D models to improve the
sharpness of the images or to design dedicated algorithms such as for vascular trees.
The obstacles concerning the development of such 3D tomographic systems are in the
increase of scatter radiations and in the large size of data files to process. Thus, success
will depend on precise correction processing and efficient reconstruction algorithms.
We also need to adapt the acquisition geometries and trajectories to the region of
interest we want to explore, for instance in cone-beam tomography.
What will the next challenge be ? 4D image reconstruction for time varying objects is
beginning to be explored such as in angiography, to study abnormal blood flow
circulation between arteries and veins, or in cardiac gated SPECT, to reduce the
blurring caused by heart motion, or in 4D image reconstruction of functional images.
We have introduced this subject among the topics of the meeting and we are sure it will
become increasingly important in the future.
vii
viii
This book is organised in four parts covering the following topics :
-cone-beam and new geometries reconstruction,
-SPECT quantitation,
-patient motion and gated SPECT,
-PET quantitation and reconstruction.
We trust this issue contents update and new insight of on-going researches in fully 3D
image reconstruction in radiology and nuclear medicine and we do hope it will
contribute to the promotion and development of this expanding field.
Pierre GRANGEAT, Chairman, and Jean-Louis AMANS, Co-editor.
ACKNOWLEDGEMENTS
The editors would particularly like to thank the authors who contributed to this issue,
the Scientific Committee for their help to the selection and the examination of the
papers, and also complementary reviewers.
We are indebted to the members of the Organizing Committee who have worked hard
to make this 1995 International Meeting on Fully Three-Dimensional Image
Reconstruction in Radiology and Nuclear Medicine a complete success, and to
Mireille Berthier who spent considerable amount of time mailing and managing data
bases. Lastly, a special thank you to all the sponsors for their financial support.
Scientific Committee
BENDRIEM, Bernard, Orsay, France,
COATRIEUX, Jean-Louis, Rennes, France,
DEFRISE, Michel, Bruxelles, Belgium,
DI PAOLA, Robert, Villejuif, France,
ERIKSSON, Lars, Stockholm, Sweden,
GARNERO, Line, Orsay, France,
GULLBERG, Grant, Salt Lake City, USA,
JASZCZAK, Ronald, Durham, USA,
KUDO, Hiroyuki, Tsukuba, Japan,
LEWITT, Robert, Philadelphia, USA,
NATTERER, Frank, Miinster, Germany,
TOWNSEND, David, Pittsburg, USA,
TROUSSET, Yves, Buc, France,
TSUI, Benjamin, Chapel Hill, USA.
Complementary reviewers
BARLAUD, Michel, Valbonne, France,
DANIELSSON, Per-Erik, Linkoping, Sweden,
GUILLAND, David, Durham, USA,
KINAHAN, Paul, Pittsburg, USA,
LI, Jianying, Durham, USA,
PARKER, Dennis, Salt Lake City, USA,
PEYRIN, Fran<;oise, Grenoble, France,
ROUX, Christian, Brest, France,
SAUER, Ken, Notre Dame, USA,
SMITH, Mark, Durham, USA,
TUY, Heang, Highland, USA,
WANG, Huili, Durham, USA,
ZENG, Larry, Salt Lake City, USA.
ix
x
Meeting Organizing Committee
ALLEMAND, Robert, LETI, Grenoble, France,
AMANS, Jean-Louis, LETI, Grenoble, France,
BOUVIER, Alain, LETI, Grenoble, France,
DARIER, Pierre, LETI, Grenoble, France,
DELORME, Nathalie, LETI, Grenoble, France,
GRANGEAT, Pierre, LETI, Grenoble, France,
GUILLEMAUD, Regis, LETI, Grenoble, France,
MAZIERE, Bernard, SHFJ, Orsay, France.
Patronage an~ financial support
Conseil General de la Savoie, CEA, CNRS, INSERM, CTI Inc.
GE Medical Systems Europe, SIEMENS Medical Systems.
