Display Settings:

Items per page

Results: 10

1.
Fig. 3

Fig. 3. From: Rotate-and-Slant Projector for Fast LOR-Based Fully-3-D Iterative PET Reconstruction.

Illustration of rotation by the three-pass method of shears, where arc-correction and a depth compression factor of 2.0 were used. Projection to unevenly-spaced LORs is efficiently accomplished by incorporating the LOR-resampling directly into the third shear of the rotator. This reduces the interpolation error while maintaining the speed advantage of this rotator.

Dan J. Kadrmas. IEEE Trans Med Imaging. ;27(8):1071-1083.
2.
Fig. 2

Fig. 2. From: Rotate-and-Slant Projector for Fast LOR-Based Fully-3-D Iterative PET Reconstruction.

The proposed rotate-and-slant projector follows three major steps. Note that Step 2, slanting to ring difference δ, involves only a 1-D slant, which is very fast and can be done repeatedly to all ring differences after a single rotation from Step 1. This makes the rotate-and-slant projector computationally efficient for fully-3-D projections to a large number of ring differences.

Dan J. Kadrmas. IEEE Trans Med Imaging. ;27(8):1071-1083.
3.
Fig. 10

Fig. 10. From: Rotate-and-Slant Projector for Fast LOR-Based Fully-3-D Iterative PET Reconstruction.

Diagrams showing the intersection of LORs (shaded) with image columns in the transverse plane (left) and with image slices in an axial plane (right), after rotation of the image matrix to angle ϕ. The area-of-overlap between LOR A and image voxel 1 is indicated (left diagram) and can be computed by the length-of-overlap between the LOR edges and voxel as indicated. The area-of-overlap in the axial plane between LOR C and image voxel 5 is similarly indicated (right diagram), and is computed based on the length-of-overlap as shown (which introduces a slight approximation in some cases as discussed in the text).

Dan J. Kadrmas. IEEE Trans Med Imaging. ;27(8):1071-1083.
4.
Fig. 7

Fig. 7. From: Rotate-and-Slant Projector for Fast LOR-Based Fully-3-D Iterative PET Reconstruction.

Quantitative analysis of image quality measures for the five reconstruction schemes studied. The resolution and contrast measures (top row) demonstrate broad similarities for each reconstruction method, with some differences in the rate of iterative recovery of these image features. The plots on the bottom row permit comparison of image background noise at matched resolution (left) or contrast (right). Fully-3-D LOR-OSEM outperformed the rebinning and conventional AW-OSEM methods, and the more volumetric projectors (rotate-and-slant, distance-driven) outperformed the ray-driven projector.

Dan J. Kadrmas. IEEE Trans Med Imaging. ;27(8):1071-1083.
5.
Fig. 8

Fig. 8. From: Rotate-and-Slant Projector for Fast LOR-Based Fully-3-D Iterative PET Reconstruction.

Projection CPU times for the TruePoint Biograph scanner, plotted as a function of the number of oblique segments, for the three projectors studied. A 128 × 128 × 81 slice image matrix was used, and the projectors mapped to 335 unevenly-spaced LORs at each of 336 angles. The rotate-and-slant projector used a depth-compression factor of 8 for this data. Processing time for the conventional projectors scaled poorly with increasing numbers of oblique segments, whereas the rotate-and-slant projector scaled very efficiently, even for the complete fully-3-D case with all segments. This is due to the manner in which the rotate-and-slant projector efficiently conserves azimuthal operations for computing 3-D projection to multiple oblique segments.

Dan J. Kadrmas. IEEE Trans Med Imaging. ;27(8):1071-1083.
6.
Fig. 6

Fig. 6. From: Rotate-and-Slant Projector for Fast LOR-Based Fully-3-D Iterative PET Reconstruction.

Example images of the Deluxe Jaszczak Phantom at 10 iterations for the five reconstruction methods studied. The smallest 4.8-mm-diameter rods are resolved for each reconstruction method, as is the smallest 9.5-mm-diameter cold sphere. Small circles of radioactivity are also visible surrounding the support rods for the spheres, which appear between the wedges of hot rods. The images for each of the reconstruction methods were visually similar, with differences in noise texture being the largest effect noted. Horizontal profiles across one row of the 7.9- and 11.1-mm-diameter rods show somewhat better peak-to-valley definition of the rods for the distance-driven and rotate-and-slant projectors as compared to the other cases. A depth-compression factor of 8 was used for the rotate-and-slant projector.

Dan J. Kadrmas. IEEE Trans Med Imaging. ;27(8):1071-1083.
7.
Fig. 9

Fig. 9. From: Rotate-and-Slant Projector for Fast LOR-Based Fully-3-D Iterative PET Reconstruction.

Reconstruction CPU times for the Advance scanner, plotted as a function of the number of oblique segments, for 4 iterations OSEM with 14 subsets and four reconstruction schemes. Each sinogram of the raw projection data had 283 unevenly-spaced LORs and 336 angles, and the reconstruction matrix was 128 × 128 × 35 slices. The first three curves are for fully-3-D LOR-OSEM, and the final curve is for Fourier rebinning followed by 2-D AW-OSEM. Using the rotate-and-slant projector with depth-compression factor of 8, total processing time for fully-3-D iterative reconstruction was similar to that for 2-D reconstruction.

Dan J. Kadrmas. IEEE Trans Med Imaging. ;27(8):1071-1083.
8.
Fig. 5

Fig. 5. From: Rotate-and-Slant Projector for Fast LOR-Based Fully-3-D Iterative PET Reconstruction.

Effect of using depth compression factors upon projection time (left) and accuracy measures (right). Here, the FWHM characterizes the axial profile of the 13-mm sphere in the NEMA phantom reconstructed image, and %RMSE provides a measure of accuracy for projections of the modified Shepp-Logan phantom at ring difference δ = 20. Projection times dropped quickly with compression factors up to about 8, whereas accuracy was largely unaffected for compression factors of 8 and below. These results indicate that using a compression factor of 4 or 8 (for a 128 × 128 image) offers significant speedup of the rotate-and-slant projector without a significant concomitant loss of accuracy.

Dan J. Kadrmas. IEEE Trans Med Imaging. ;27(8):1071-1083.
9.
Fig. 4

Fig. 4. From: Rotate-and-Slant Projector for Fast LOR-Based Fully-3-D Iterative PET Reconstruction.

Example images showing the depth-dependent behavior of the approximations introduced by the use of depth-compression. These images show the absolute value percent error of a simulated disc phantom one slice thick, centered in the field-of-view, and reconstructed using fully-3-D OSEM with depth-compression factors ranging from 2 to 64 as indicated. The top images share the same greyscale as shown; the greyscales for the bottom images were normalized individually, with average percent error shown in parenthesis. Depth-compression effectively compresses the depth information into coarse slabs, where the center of each slab is unaffected and the upper- and lower-edges of the slab experience the greatest approximation. Since depths map to radii in the reconstructed image, each depth-compressed slab produces a concentric ring on these error images. The extreme case of a depth-compression factor of 128 (equal to the image dimension) would be analogous to SSRB, where there would be one “ring” with little error at the center but very large error at the edge.

Dan J. Kadrmas. IEEE Trans Med Imaging. ;27(8):1071-1083.
10.
Fig. 1

Fig. 1. From: Rotate-and-Slant Projector for Fast LOR-Based Fully-3-D Iterative PET Reconstruction.

Coordinate system (s, ϕ, z, δ) used to parameterize an LOR for a generic ring PET tomograph. The z coordinate describes the axial position of the midpoint of the LOR, which falls at the point of closest approach to the central axis of the tomograph. Note that the length of the LOR (here denoted Δy, where the y-direction is defined perpendicular to s within the transaxial plane), is dependent upon s. As a result, the polar angle θ is not only dependent upon the ring difference δ, but there is also a secondary dependence upon s. For cylindrical ring PET tomographs, the LORs grouped into a parallel projection at a given angle are unevenly spaced in s. The diagram at right also shows interleaving of LORs from adjacent azimuthal angles (solid and dashed lines), which have been merged into a single angular bin, effectively halving the number of angular samples but doubling the transverse sampling in each.

Dan J. Kadrmas. IEEE Trans Med Imaging. ;27(8):1071-1083.

Display Settings:

Items per page

Supplemental Content

Recent activity

Your browsing activity is empty.

Activity recording is turned off.

Turn recording back on

See more...
Write to the Help Desk