A general fan-beam reconstruction algorithm for free-form trajectories

ADVANCED NUCLEAR INSTRUMENTATION AND DETECTION

A general fan-beam reconstruction algorithm for free-form trajectories

LI Liang，

CHEN Zhi-Qiang，

WANG Ge，

KANG Ke-Jun

Nuclear Science and Techniques

Vol.16, No.3

pp.171-176

Published in print 01 Jun 2005

CLC：TP301.6

23400

In this paper we develop a general exact fan-beam reconstruction algorithm for free-form trajectories not only closed but also unclosed, based on the fan-beam reconstruction formula recently developed by Noo et al.. A mathematical proof is then provided with the geometrical explanation of equi-spatial detectors. With this algorithm we can obtain exact region of interest (ROI) reconstruction if and only if every projecting line passing through the ROI intersects the free-form source trajectory, when the projections are not truncated. Furthermore, under the condition that the source-to-detectors distance changes slowly enough relative to the length itself, we obtain a very good approximate reconstruction algorithm, which is the same as the algorithm of the circular trajectory except that the source-to-detectors distance is a function of the rotation angle. Then the algorithms are tested using the Shepp-Logan phantom and the experiment shows that the algorithms can get perfect numerical results.

TomographyFan-beamImage reconstructionRegion of Interest (ROI)

References

[1]

Herman G T, Naparstek A. SIAM J Appl Math, 1977, 33: 511-533

[2]

Horn B K P. Proc IEEE, 1979, 67: 1616-1623

[3]

Weinstein F S. J Opt Soc Amer, 1980, 70: 931-935

[4]

Smith B D. IEEE Trans Med Imag, 1985, MI-4: 177-184

[5]

Hu H, Gullberg G T, Kruger R A. IEEE Trans Med Imag, 1988, 7(3): 233-238

[6]

Wang Ge, Lin Tein-Hsiang, Cheng Ping-chin. IEEE Trans Med Imag, 1993, 2(4): 543-547

[7]

Noo F, Defrise M, Clackdoyle R et al. Phys Med Biol, 2002, 47: 2525-2546

[8]

Parker D L. Med Phys, 1982, 9: 254-257

[9]

Kudo H, Noo F, Defrise M et al. “

New super-short-scan algorithm for fan-beam and cone-beam reconstruction

”, Records of the 2002 IEEE Nuclear Science and Medical Imaging Symposium, paper M5-3, 2003

Baidu Scholar

Google Scholar

[10]

Katsevich . SIAM J Appl Math, 1996, 56(1): 167-191

[11]

Yu Hengyong, Wang Ge. Med Phys, 2004, 31(6): 1357-1362

[12]

Proksa R, Köhler T, Grass M et al. IEEE Transactions on Medical Imaging, 2000, 19(9): 848-863

[13]

Turbell H. “Cone-beam reconstruction using filtered backprojection” [M], SE-581 83 Linkoping, Sweden, 2001: 19-23

[14]

Katsevich . SIAM J Appl Math, 2002, 62(7): 2012-2026

[15]

Katsevich . Int'l J of Math and Math Sci, 2003, 21: 1305-1321

[16]

Katsevich . SPIE Medical Imaging, San Diego, 2003: 663-674