Reconstruction from Uniformly Attenuated SPECT Projection Data Using the DBH Method Page: 14 of 21
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Fig. 9: The 95% confidence interval for the pixel value at the origin. The horizontal axis indicates six tests: Tests 1, 2, 3 for non-truncated data with total
counts of 1X105, 5x105 and 1X106, and Tests 4, 5, 6 for truncated data with total counts of 1X105, 5x105 and 1X106 For each test, the mean value (dot)
and the confidence limits (*) are shown. The limits (*) of the 95% confidence interval are tabulated in Table 1.
Fig. 10: Reconstructed images from parallel-beam, truncated noise-free (left), and noisy (right) data. The grayscale is [0.15, 0.45].
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Fig. 11: Variance images for different noise levels with truncation. The total counts equal 1x105, 5 x105 and 1x106, from left to right. The grayscale is [0,
0.0339] for all the three images.
5x 105 and 1x 106, respectively. The same trend as in the non-truncated case can be observed. The higher the
total number of counts, the lower the ensemble variance and the narrower the confidence interval. In other
words, greater precision is expected when we increase the counts. This is shown graphically in Fig. 9. Note
that the true value at the origin was 0.3. The results show differences between the reconstruction of
truncated and non-truncated data in both the bias and the variance. For the non-truncated cases the bias and
precision improve with the increase in the total counts whereas for the truncation cases the precision
improves with increased counts but the bias appears to become worse.
C. Fan-beam truncated short-scan data with and without noise
Equation (26) indicates that the data range required for H, (s) is the same interval as for h(t), indicating
that the DBP image f(x,y) in the inner disk of Fig. 3 is sufficient for reconstructing the original
image f(x, y). In order to ensure a numerically stable inversion using (26), the DBH operation has to be
conducted in a larger area than the support of f(x, y). Since the fan-beam short-scan reconstruction using
the DBH method with and without truncation is virtually identical within the truncated FOV, we only show
in this paper the simulation for the reconstruction of truncated short-scan data. In our computer simulations,
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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. (https://digital.library.unt.edu/ark:/67531/metadc901800/m1/14/: accessed May 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.