Methods and apparatus for fast divergent beam tomography

52 Pages·2013·2.7 MB·English

US006771732B2
(12) United States Patent (10) Patent N0.: US 6,771,732 B2
Xiao et al. (45) Date of Patent: Aug. 3, 2004
(54) METHODS AND APPARATUS FOR FAST “Fast Calculation of Multiple Line Integrals”; Brandt et al;
DIVERGENT BEAM TOMOGRAPHY SIAMJ. Sci. Comput, vol. 20, No. 4, pp. 1417—1429; 1999.
Multi—Resolution Mixed Radix Quadtree SAR Image
(75) Inventors: Shu Xiao, Sunnyvale, CA (US); Yoram Focusing Algorithms; Oh et al; Third Annual Federated
Bresler, Urbana, IL (US); David C. Laboratory Symposium on Advanced Sensors; pp. 139—143;
Munson, J r., Champaign, IL (US) Feb. 2—4, 1999.
“Iterative Techniques for Projection and Back—Projection”;
(73) Assignee: The Board of Trustees of the
Per—Erik Danielsson; Institute of Technology, Linkopings
University of Illinois, Urbana, IL (US)
Universilet; pp. 1—39; Jun. 1997.
( * ) Notice: Subject to any disclaimer, the term of this “Three—dimensional Reconstruction from Cone—beam Data
patent is extended or adjusted under 35 in O(N3log N)Time”; Axelsson et al.; Phys. Med. Biol.; 39,
U.S.C. 154(b) by 64 days. pp. 477—491; 1994.
“A Fast Discrete Approximation Algorithm for the Radon
(21) Appl. No.: 10/190,295 Transform”; Martin Brady; SIAM J. Comput, vol. 27, No. 1,
pp. 107—119; Feb. 1998.
(22) Filed: Jul. 5, 2002
(65) Prior Publication Data (List continued on next page.)
US 2003/0161443 A1 Aug. 28, 2003 Primary Examiner—David Bruce
(74) Attorney, Agent, or Firm—Greer, Burns & Crain, Ltd.
Related US. Application Data
(60) Provisional application No. 60/360,390, ?led on Feb. 28, (57) ABSTRACT
2002.
A fast method for divergent-beam backprojection is pro
posed for generating an electronic image from a prepro
(51) Int. Cl.7 ................................................ .. A61B 6/03
cessed divergent-beam sonogram, the sinogram being a
collection of divergent beam projections. The method con
(52) US. Cl. ............................ .. 378/4; 378/15; 378/901
sists of the following steps: subdividing the sinogram into
multiple sub-sinograms; performing a Weighted backprojec
(58) Field of Search ............................. .. 378/4, 15, 901
tion of said sub-sinograms, to produce multiple correspond
(56) References Cited ing sub-images; and aggregating said sub-images to create
the electronic image. The subdivision of the sinogram into
U.S. PATENT DOCUMENTS
sub-sinograms can be performed in a recursive manner. A
5,778,038 A 7/1998 Brandt et a1. ................ .. 378/4 dual of the proposed method provides a fast means for
5,805,098 A 9/1998 McCorkle .................. .. 342/25 reprojecting an electronic image, i.e., generating a
divergent-beam sinogram from the image. These methods
6,151,377 A 11/2000 Nilsson . . . . . . . . . . .. 378/4
6,263,096 B1 * 7/2001 Boag et al. .. .. 382/128 are applicable to fan-beam and cone-beam tomography
6,282,257 B1 * 8/2001 Basu et al. 378/15 utilizing a variety of scanning trajectories, including spiral.
6,307,911 B1 * 10/2001 Basu et al. ................. .. 378/15 These methods do not require rebinning, and offer speedups
6,332,035 B1 * 12/2001 Basu et al. ............... .. 382/128 similar to the FFT When compared to conventional back
6,351,548 B1 * 2/2002 Basu et al. ............... .. 382/128 projection and reprojection algorithms. Substantial compu
OTHER PUBLICATIONS tational savings are obtained Without perceptible degrada
“Cone—Beam Reconstruction Using Filtered Backprojec tion or signi?cant loss of numerical accuracy.
tion”; Henrik Turbell; Institute of Technology, Linkopings
Universitet; pp. 1—169; Feb. 2001. 44 Claims, 35 Drawing Sheets
D5 SEVUGRAM (UR SL'BSINOGRLVD
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US 6,771,732 B2
Page 2
OTHER PUBLICATIONS “Error Analysis and Perforarnnce Optimization of Fast Hier
archical Backprojection Algorithrns”; Basu et al; ; IEEE
“Fast Feldkarnp Reconstruction”; Turbell, et al,; Linkopings
Transactions on Image Processing; vol. 10, No. 7; pp.
Universitel; Dec. 15, 1998.
1103—1117; Jul. 2001.
“The PI—FAST Method for Approximate Helical
Cone—bearn Reconstruction”; Turbell et al.; Proc. Sixth Int. “O(N3log N) Backprojection Algorithm for the 3—D Radon
Meeting on Fully Three—Dirnensional Image Reconstruction
Transforrn”; Basu et al. .; IEEE Transactions on Medical
in Radiology and Nuclear Med.; Asilornar, Paci?c Grove,
Imaging; vol. 21, No. 2; pp. 76—88; Feb. 2002.
CA; Oct. 30—Nov. 2, 2001.
“Multifrequential Algorithm for Fast 3D Reconstruction”; Seger et al.; “Real Time SAR Processing of LoW Frequency
Rodet et al.; Proc. Sixth Int. Meeting on Fully Three—Di Ultra Wide Band Radar Data”; European Conference on
rnensional Irnage Reconstr. In Radiology and Nuclear Med., Synthetic Aperture Radar; Friedrichshafen, Gerrnany; pp.
Asilornar, Paci?c Grove, CA; Oct. 30—Nov. 2, 2001. 489—492; May 1998.
“A Multilevel Dornain Decornposition Algorithm for Fast
0(N2 log N ) Reprojection of Tornographic Irnages”; Boag Hellsten et al; Synthetic—Aperture Radar Processing Using
et al.; IEEE Transactions on Image Processing; vol. 9, No. Fast Factorised Backprojection; European Conference on
9; pp. 1573—1582; Sep. 2000. Synthetic Aperture Radar; Friedrichshafen, Gerrnany; pp.
“O(N2log2N) Filtered Backprojection Reconstruction Algo 753—756; 2000.
rithrn for Tornography”;Basu et al.; IEEE Transactions on
Image Processing: vol. 9, No. 10:pp. 1760—1773; Oct. 2000. * cited by exarniner
U.S. Patent Aug. 3, 2004 Sheet 1 0f35 US 6,771,732 B2
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U.S. Patent Aug. 3, 2004 Sheet 2 0f35 US 6,771,732 B2
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