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Comparison of sinogram- and image-domain penalized-likelihood image reconstruction estimatorsa)
a)This is a greatly expanded and revised version of a conference proceedings paper from the 1st International Meeting on Image Formation and Reconstruction in CT.
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10.1118/1.3594547
/content/aapm/journal/medphys/38/8/10.1118/1.3594547
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/38/8/10.1118/1.3594547
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Matrices R S for parallel (left) and fanbeam (right) geometries. The prominent diagonal line corresponds to a given channel’s own contribution to the assessment of the penalty. The energy in the bands midway to the corners corresponds to contributions of the conjugate rays.

Image of FIG. 2.
FIG. 2.

Typical line profiles through the penalty matrix for parallel (left) and fanbeam (right) geometries. The pair of spikes corresponds to contributions of the ray of interest and of its conjugate partner.

Image of FIG. 3.
FIG. 3.

Plot of R S,jk for a fixed j for a range of k corresponding to about three projection views.

Image of FIG. 4.
FIG. 4.

Plot of R S,jk for a fixed j for a range of k corresponding to about ten channels on either side of j. This is a zoomed view of the central feature in Fig. 3.

Image of FIG. 5.
FIG. 5.

Plot of the approximate R S,jk we employ for a fixed j for a range of k corresponding to about ten channels on either side of j.

Image of FIG. 6.
FIG. 6.

Numerical ellipse phantom used to determine image properties.

Image of FIG. 7.
FIG. 7.

Typical noisy images for (left) image-domain penalty (center) “exact” sinogram-domain penalty (right) approximate sinogram-domain penalty.

Image of FIG. 8.
FIG. 8.

Local impulse responses in the hot circle for (left) image-domain penalty (center) “exact” sinogram-domain penalty (right) approximate sinogram-domain penalty.

Image of FIG. 9.
FIG. 9.

Horizontal (left) and vertical (right) profiles through the LIRs for image domain, exact sinogram domain, and approximate sinogram domain.

Image of FIG. 10.
FIG. 10.

Square system matrix: resolution-variance tradeoffs for points at the center of the phantom and at the center of the “hot” and “cold” disks for reconstruction of a 128 × 128 image from a 128 bin × 128 angle sinogram. We show results calculated using both the brute-force approach (“Empirical”) and the analytic expressions (“Analytical”) for both the sinogram- and image-domain approaches.

Image of FIG. 11.
FIG. 11.

Overdetermined system matrix: resolution-variance tradeoffs for points at the center of the phantom for reconstruction on a 256 × 256 grid from sinograms of 256 bins and 256, 384, and 512 angles.

Image of FIG. 12.
FIG. 12.

Underdetermined system matrix: resolution-variance tradeoffs for points at the center of the phantom and at the center of the “hot” and “cold” disks for reconstruction of a 256 × 256 image from a 128 bin × 128 angle sinogram. Despite the problem being underdetermined, both image-domain and sinogram-domain approaches still perform similarly.

Image of FIG. 13.
FIG. 13.

Resolution-variance tradeoffs for points at the center of the cold and hot disks and at the center of the phantom for reconstruction of an image from a 672 bin × 1160 angle fanbeam sinogram. Pixel size is 0.75 mm.

Image of FIG. 14.
FIG. 14.

Reconstructed images of shoulder and abdomen slices using the image- and sinogram-domain approaches. Resolution has been matched between each pair of images by comparing profiles, as shown in Fig. 16. (Window = 100, Level = 0).

Image of FIG. 15.
FIG. 15.

Shoulder phantom showing where the profiles were examined for resolution matching (along the three small white lines shown to the right of the lung) and where the noise was sampled in a relatively uniform ROI (near the upper left).

Image of FIG. 16.
FIG. 16.

Profile through the bright enhanced vessel in the shoulder slice showing that resolution has been well matched between the images reconstructed by the image- and sinogram-domain approaches.

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/content/aapm/journal/medphys/38/8/10.1118/1.3594547
2011-07-29
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Comparison of sinogram- and image-domain penalized-likelihood image reconstruction estimatorsa)
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/38/8/10.1118/1.3594547
10.1118/1.3594547
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