The M1 configuration has evenly interleaved MTR and HTR detectors. We considered three sub-configurations that were obtained by employing 24, 16, or 12 HTR detectors (representing 1/2, 1/3, and 1/4 of the total number of detector modules) and identified them as M1–1/2, M1–1/3, M1–1/4, respectively. All detectors were first assumed to have the same DE so that for all LORs. Two noise levels were simulated for Phantom 1, corresponding to 300K and 1,000K total counts (1K = one thousand). Figure 4 shows the CRC-versus-BV curves obtained for all sources of the phantom for the M1–1/4 configuration from the 1,000K data as the number of iterations varies. There are no significant differences between the curves, which is also true for other symmetrical configurations (not shown). Therefore, below for S and M1 configurations we present only the curve averaged over all the sources.

Figure 4. The CRC-versus-BV curves for the nine sources of Phantom 1 for the M1–1/4 configuration with 1,000K events. The MTR and HTR detectors have the same DE. The insert shows Phantom 1 (35 cm diameter) and the M1 configuration of the scanner (78 cm diameter). For visuality, they are not shown at the same scale.

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Figure 5(a) shows the resulting average CRC-versus-BV curves for various S and M1 configurations from the 300K data. As expected, at the same BV the S-100 curve has the highest CRC and the S-528 curve the lowest. Also, the CRC of the M1 configuration decreases as the number of HTR detectors decreases. At the same BV, the CRC of M1–1/2 is slightly higher than the average of the CRCs of S-100 and S-528. Interestingly, it is empirically found to be very similar to the CRC-versus-BV curve obtained by S-220. Figure 5(b) shows the CRC-versus-BV curves for the 1,000K data. The observations made above with the 300K data remain applicable but the vertical gaps between the curves are smaller. Comparing the curves in figures 5(a) and (b) for the same configuration, we observe that the latter has a small BV range, has a smaller BV and larger CRC at the same iteration number, generally has a large CRC at the same BV, and appears to converge toward a larger CRC. The first two observations can be attributed to the faster convergence rate when reconstructing higher-count data. The other two observations are consistent with that quantitatively more accurate images can be obtained from higher-count data. Disregarding S-220, curves in figure 5(a) (or figure 5(b)) similarly suggest that, when working with data having the same number of events, a faster convergence rate is achieved with configurations that employ more HTR detectors.

Figure 5. The average CRC-versus-BV curves of Phantom 1 obtained for M1, S-100, and S-528 configurations for 300K (a), (c), and 1,000K (b), (d). In (a) and (b), the MTR and HTR have the same DE, and the curve of M1–1/2 is empirically found to be similar to that of S-220. In (c) and (d), DEs are scaled according to the detector thickness, and same-duration data (see text) are considered. The insert in (b) shows Phantom 1 (35 cm diameter) and the M1 configuration of the scanner (78 cm diameter). For visuality, they are not shown at the same scale.

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As discussed above, 100 ps CTR was often achieved by using crystals that are shorter than 10 mm and most current clinical systems employ 20 mm thickness crystals. In the second experiment, we accordingly assumed that the HTR and MTR detectors have 10 mm and 20 mm thickness, respectively. Based on these thicknesses and the attenuation coefficient of L(Y)SO for 511 keV gamma rays, we estimated that the DE of the HTR detector is 0.7 times that of the MTR detector. Hence, the type-M, type-H, and type-HM LORs will be assigned with equal to 1.0, 0.49, and 0.7, respectively. Again, data containing 300K and 1,000K events were generated for S-528. For other configurations, data for the same durations were simulated; however, despite having fewer events they are still identified as 300K and 1,000K data. For distinction, we will refer to the previous experiments as 'same-count' and the current ones as 'same-duration'. Figures 5(c) and (d) plot the average CRC-versus-BV curves obtained for the 300K and 1,000K data, respectively. Comparing figure 5(c) with figure 5(a) (or figure 5(d) with figure 5(b)) shows that, except for S-528, at the same iteration number the CRCs (BVs) of all configurations have decreased (increased). At the same BV, S-100, and M1 now offer considerably less improvement in CRC over S-528. Moreover, after a sufficient number of iterations the M1–1/2 curve can reach higher CRCs at the same BV than does the S-100 curve. This suggests that, compared to the latter, the former has a slower convergence rate (due to a larger effective CTR of about 220 ps as demonstrated in figures 5(a) and (b)) but at convergence it can yield quantitatively more accurate images. Hence, as stipulated above, the benefit offered by the higher CTR of the HTR detector is now diminished due to its lower DE.

Figure 6 shows sample images obtained for Phantom 1 from the 300K data. To reduce the dependence on the number of iterations used, these images have approximately the same BV of 0.5. Also, the images were displayed by using the same gray-level scale. Subjectively, in agreement with the above observations, in both the same-count and same-duration experiments the S-100 image has the best quality (best visibility of the sources) and the S-528 image the worst (worse visibility of the sources). By comparing the bottom-row images to the top-row images, we observe increased image noise when the lower DE of the HTR detector is accounted for. This is most evident with S-100 because its DE is diminished the most.

Figure 6. From left to right are images obtained for Phantom 1 with the S-528, M1–1/4, M1–1/3, M1–1/2, and S-100 configurations, from the 300K data in the same-count (top row) and same-duration experiments (bottom row). For these images, The images are displayed using the same gray-level scale.

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Figure 7 shows sample images obtained for Phantom 2 from the 300K data in the same-duration experiment. Again, the BV values of these images are approximately 0.5. Subjectively, the 2 mm sources (smallest sources) cannot be resolved with all configurations. The 4 mm sources (second smallest sources) are readily visible in the M1–1/2 and S-100 images and are border-line visible in the M-528 image. Overall, the S-100 image is the best, and the S-528 image is the worst. The quality of the M1 images is superior to that of the S-528 image, with the M1–1/2 image comparing favorably with the S-100 image.

Figure 7. From left to right are images () obtained for Phantom 2 with the S-528, M1–1/4, M1–1/3, M1–1/2, and S-100 configurations, from the 300K data in the same-duration experiment. The images are displayed using the same gray-level scale.

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Below, we will consider the same-duration experiment that more realistically considers the lower DE of the HTR detector. In this case, type-H LORs have the lowest detection sensitivity and type-M LORs have the highest. When comparing two CRC-versus-BV curves, we examine their CRC values at the same BVs, and a curve is said to be above (below) another, and better than (worse than) another if its CRC values are greater (smaller). Also, the gap between the two curves refers to the difference in their CRC values at the same BV. When the gap between two curves is small, they are said to be comparable or similar.

As the M2 and M3 configurations have asymmetrical distributions of the two detector types, we expect them to yield nonuniform image properties. This is illustrated in figure 8 which shows the density maps for the three LOR types passing through the image pixels for the M2 and M3 configurations. Take M2 as an example, pixels in the lower (upper) half of the FOV are sampled predominantly by type-H (type-M) LORs and type-HM LORs, and pixels in the middle are predominantly by type-HM LORs. Below in figures 9 and 11, Mx-Dn designates the CRC-versus-BV curve obtained for source Dn (n = 0–8) by the Mx (x = 2–5) configuration. Figure 9(a) compares the curves obtained by M2 with those obtained by S-100 and S-528 for Phantom 1, from the 300K data in the same-duration experiment. At the same BV, the M2-D6, M2-D7, and M2-D8 curves have higher CRCs than the S-528 curve, with M2-D7 having the highest CRC, approaching that of S-100. This is consistent with the fact that these sources are in the lower half of the FOV that is preferentially sampled by type-H LORs (especially D7). After a sufficient number of iterations, curves obtained for other sources are comparable with the S-528 curve. These sources are in regions that are sampled by only type-M and type-HM LORs and where the lower DE of the HTR detector has offset the benefit offered by its better CTR. Figure 9(b) similarly shows the CRC-versus-BV curves obtained by M3 for Phantom 1, from the 300K data in the same-duration experiment. Compared to the M2 curves in figure9(a), as fewer HTR detectors are used the M3 curves are worse in general. Now, only the M3-D8 curve is above the S-528 curve; all other curves are similar.

Figure 8. Density maps of type-H (a), Type-M (b), and type-HM (c) LORs passing through each image pixel for the M2 (top row) and M3 (bottom row) configurations.

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Figure 9. The CRC-versus-BV curves obtained for M2 (a) and M3 (b), in comparison with S-100 and S-528, from 300K-counts data in the same-duration experiment. The insert shows Phantom 1 (35 cm diameter) and the configurations of the scanner (78 cm diameter). For visuality, they are not shown at the same scale.

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Figure 10 shows the resulting images obtained for Phantoms 1 and 2, with the BV value equals to 0.5 approximately. The subjective quality of Phantom 1 images is consistent with the observations made above from the CRC-versus-BV curves: With respect to the S-528 image, visually the M2 image shows better quality in the lower FOV; elsewhere, it has comparable quality, but the center region is arguably inferior. The M3 image shows better (worse) quality in the lower-right (upper-left) quadrant of the FOV. Similarly, with Phantom 2 images we observe improved visibility for the 4 mm sources with M2 and M3 with respect to S-528 when they are placed in the favorable regions of these configurations.

Figure 10. Top row: From left to right are images () obtained for Phantom 1 (35 cm diameter) with S-528, M2, M3, and S-100 configurations, from 300K data in the same-duration experiment. The phantom is placed at the center of the scanner. Bottom row: Images with obtained for Phantom 2 (30 cm diameter) that is placed at the center of the FOV for the S-518 and S-100 configurations, in the lower half for the M2 configuration, and the lower-right quadrant for the M3 configuration. The images are displayed using the same gray-level scale. The M2 and M3 configurations of the scanner (78 cm diameter) are also shown for reference. Note that the images and the scanner configurations are not displayed at the scale.

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The M1–1/2 and M2 configurations both employ 24 HTR detectors. Comparison of figures 9(a) and 5(c) shows that the best CRC-versus-BV curve (and most CRC-versus-BV curves) obtained with M2 is no better than (are inferior to) the average CRC-versus-BV curve obtained with M1–1/2. The M1–1/4 and M3 configurations both employ 12 HTR detectors. In this case, a comparison of figures 9(b) and 5(d) shows that the best CRC-versus-BV curve of M3 is better than the average CRC-versus-BV curve of M1–1/4. These observations suggest that the symmetric configurations are preferred when using relatively many HTR detectors but the asymmetric configurations may offer better image quality in specific regions when using relatively few HTR detectors. However, this observation is likely to be dependent on the detailed tradeoff characteristics between the improved CTR and diminished DE offered by the HTR detector.

We observed above that replacing MTR detectors with HTR detectors does not necessarily lead to improved image quality because the benefit offered by better CTR can be offset by diminished DE. Thus, if we are interested in improving the quality of a small region, it may be achieved by using a small number of HTR detectors to create type-H LORs for pixels in this region while maintaining the overall physical sensitivity of the system. For the purpose of demonstration, we examine an off-center focus region and a central focus region with the M4 and M5 configurations, respectively. We note that the D4 (D0) source of Phantom 1 is located inside the focus area of M4 (M5).

Figure 11(a) shows the CRC-versus-BV curves obtained by M4 from the 300K data in the same-duration experiment. For M4, the D4 curve is the best, which is consistent with the fact that D4 is in the focus area. With respect to the S-528 curve, the M4-D4 curve is noticeably higher and approaches the S-100 curve at large BV. In addition, it is slightly below the best M2 curves but is above the M3 curves shown in figure9. The D2 and D6 sources are seen by one pair of the HTR detector modules. Naturally, their curves are below M4-D4. However, they are still above S-528 and are slightly better or similar to the best M3 curve in figure9. For other sources, their curves are comparable with the S-528 curve. Therefore, based on the CRC-versus-BV evaluation the M4 configuration that employs only four HTR detector modules yields similar- or better-quality images than the M2 and M3 configurations that employ more than twelve HTR detector modules. Figure 11(b) shows the CRC-versus-BV curves obtained by M5. The observations made above with the M4 apply as well. Figure 12 compares the images obtained for Phantom 1 from the 300K data in the same-duration experiment by the M4, M5, S-528, and S-100 configurations. The results are consistent with the CRC-versus-BV assessment. Compared with S-528 (S-100), source visibility in the focus area of M4 and M5 is better (similar).

Figure 11. The CRC-versus-BV curves obtained for M4 (a) and M5 (b), in comparison with S-100 and S-528, from 300K data in the same-duration experiment. The insert shows Phantom 1 (35 cm diameter) and the configurations of the scanner (78 cm diameter). For visuality, they are not shown at the same scale.

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Figure 12. From left to right are images () obtained for Phantom 1 (35 cm diameter) with S-528, M4, M5, and S-100 configurations, from 300K data in the same-duration experiment. The circles in the M4 and M5 images indicate the focus areas of these configurations. The images are displayed using the same gray-level scale.

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The above result indicates that it is feasible to use a small number of HTR detectors to boost the quality in a focus area without sacrificing quality in other regions. Therefore, we also aggressively consider using ultra-high time-resolution (UHTR) detectors that have a 10 ps CTR and the same DE as the HTR detector. Below, we will use M4–10 and M4–100 (M5–10 and M5–100) to designate the M4 (M5) configurations employing HTR and UHTR detectors respectively. Figure 13 compares the images obtained for Phantom 2 by S-100 and S-528 with those obtained by M4 and M5. In the latter cases, the phantom was positioned in such a way that the 4 mm sources group was inside their focus area. Again, the visibility of the 4 mm sources group in the M4–100 and M5–100 images is considerably superior to that of the S-528 image and slightly inferior to that of the S-100 image. In M4–10 and M5–10 images, the visibility of the 4 mm sources group is arguably better than that of the S-100 images.

Figure 13. Reconstructed images obtained for Phantom 2 (30 cm diameter) from the 300K data in the same-duration experiment with S-528, S-100, M4, and M5 employing HTR detectors (M4–100 and M5–100), and M4 and M5 employing UHTR detectors (M4–10 and M5–10). For the S-100 and S-528 configurations, the phantom is placed at the center of the FOV. For the M4 and M5 configurations, the phantom is placed in positions where its 4 mm sources are in the focus regions of these configurations. The images are displayed using the same gray-level scale.

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