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Reconstruction from Uniformly Attenuated SPECT Projection Data Using the DBH Method
Qiu Huang, Jiangsheng You, Gengsheng L. Zeng, and Grant T. Gullberg
Abstract-An algorithm was developed for the two-dimensional (2D) reconstruction of truncated and
non-truncated uniformly attenuated data acquired from single photon emission computed tomography
(SPECT). The algorithm is able to reconstruct data from half-scan (1800) and short-scan (1800 + fan angle)
acquisitions for parallel- and fan-beam geometries, respectively, as well as data from full-scan (360)
acquisitions. The algorithm is a DBH method, which involves the backprojection of differentiated
projection data followed by an inversion of the finite weighted Hilbert transform. The kernel of the inverse
weighted Hilbert transform is solved numerically using matrix inversion. Numerical simulations confirm
that the DBH method provides accurate reconstructions from half-scan and short-scan data, even when
there is truncation. However, as the attenuation increases, finer data sampling is required.
Index Terms-Image reconstruction, attenuation, SPECT, truncation, fan-beam, half-scan, short-scan
Quantitative studies in single photon emission computed tomography (SPECT) are important in clinical
diagnosis and treatment. However, there are problems which can make it difficult to perform quantitative
SPECT imaging. Attenuation is a major degradation factor in image quality . Truncated measurements,
which occur when the camera field of view (FOV) is smaller than the patient imaged, cause artifacts in the
reconstructed image [2, 3]. Also, to minimize the loss in camera resolution as the source-to-detector
distance increases, there is considerable interest to perform acquisitions close to the organ of interest such
as in breast imaging where anterior scanning close to the breast is desired. Another advantage of anterior
scanning is that a half-scan (1800) or a short-scan (1800 + fan angle) can be implemented that covers the
least attenuated half circles. Here we investigate a method that reconstructs the image from uniformly
attenuated data measured over a half-scan acquisition for parallel-beam geometry and a short-scan
acquisition for fan-beam geometry, and allows use of a relatively small detector with projections truncated
at some view angles.
In the past three decades, much research has been performed in developing iterative and analytical
attenuation compensation algorithms for different data acquisition geometries. Iterative algorithms, such as
those in [4-12], have the potential to utilize better models of the imaging system that include various
physical factors and complicated data acquisition geometries but require significant amount of computation
compared to analytical methods. Whereas, analytical methods, such as those in [13-15], treat the projection
data as perfect line integrals and the reconstruction can be carried out efficiently using mathematically
Submitted to IEEE Trans. on Med. Imag., 2008.
This work was supported in part by the Director, Office of Science, Office of Biological and Environmental Research, Medical Science Division of the U. S.
Department of Energy under Contract No. DE-AC02-05CH11231 and in part by Public Heath Service grant R01EB000121 awarded by the National Institute of
Biomedical Imaging and Bioengineering, Department of Health and Human Services.
Qiu Huang is with the E. O. Lawrence Berkeley National Laboratory, One Cyclotron Road, Mail Stop 55R0121, Berkeley, CA 94720, USA (phone: 510-
495-2714; fax: 510-486-4768; e-mail: email@example.com).
Jiangsheng You is with Cubic Imaging LLC, 18 Windemere Dr, Andover MA 01810, USA (e-mail: firstname.lastname@example.org).
Gengsheng L. Zeng is with the Utah Center for Advanced Imaging Research (UCAIR), Department of Radiology, University of Utah, 729 Arapeen Drive,
Salt Lake City, UT 84108, USA (e-mail: email@example.com).
Grant T. Gullberg is with the E. O. Lawrence Berkeley National Laboratory, One Cyclotron Road, Mail Stop 55R0121, Berkeley, CA 94720, USA (e-mail:
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Huang, Qiu; You, Jiangsheng; Zeng, Gengsheng L. & Gullberg, Grant T. Reconstruction from Uniformly Attenuated SPECT Projection Data Using the DBH Method, article, March 20, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc901800/m1/1/: accessed January 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.