Figure 1.
The proposed hyper-parameter selection approach.
Figure 1.
The proposed hyper-parameter selection approach.
Figure 2.
The original XCATphantom data used to simulate input projection data for the experiments. Cross-sectional slices are shown in transverse, coronal and sagittal planes.
Figure 2.
The original XCATphantom data used to simulate input projection data for the experiments. Cross-sectional slices are shown in transverse, coronal and sagittal planes.
Figure 3.
Cross-sectional images from (a) the exact phantom image, (b) the FDK algorithm and (c) the AwPCSD algorithm with randomly chosen hyper-parameters ().
Figure 3.
Cross-sectional images from (a) the exact phantom image, (b) the FDK algorithm and (c) the AwPCSD algorithm with randomly chosen hyper-parameters ().
Figure 4.
The probability mass of all the hyper-parameter configurations after 25 iterations of the proposed Hedge-based algorithm (T = 25–50).
Figure 4.
The probability mass of all the hyper-parameter configurations after 25 iterations of the proposed Hedge-based algorithm (T = 25–50).
Figure 5.
Cross-sectional images from: (a) the exact phantom, (b) reconstruction with the best hyper-parameter configuration ( and ), and (c) reconstruction with the worst hyper-parameter configuration ( and ). The display window is [0–0.02].
Figure 5.
Cross-sectional images from: (a) the exact phantom, (b) reconstruction with the best hyper-parameter configuration ( and ), and (c) reconstruction with the worst hyper-parameter configuration ( and ). The display window is [0–0.02].
Figure 6.
Cross-sectional images from: (a) the exact phantom image, (b,c) are reconstructed images using the AwPCSD algorithm with best hyper-parameters from Cross-Validation and Hedge-based approaches, respectively.
Figure 6.
Cross-sectional images from: (a) the exact phantom image, (b,c) are reconstructed images using the AwPCSD algorithm with best hyper-parameters from Cross-Validation and Hedge-based approaches, respectively.
Figure 7.
One dimensional profile plots along pixel numbers 25 to 97 of the reconstructed images from two hyper-parameter selection methods along one arbitrary row of the images, in comparison with the exact image.
Figure 7.
One dimensional profile plots along pixel numbers 25 to 97 of the reconstructed images from two hyper-parameter selection methods along one arbitrary row of the images, in comparison with the exact image.
Figure 8.
Cross-sectional slices of (a) the exact phantom, (b,c) are the reconstructed images from the best ( and ) and worst ( and ) hyper-parameters found from the proposed approach with new settings ( and 5% threshold), respectively. The display window is [0–0.02].
Figure 8.
Cross-sectional slices of (a) the exact phantom, (b,c) are the reconstructed images from the best ( and ) and worst ( and ) hyper-parameters found from the proposed approach with new settings ( and 5% threshold), respectively. The display window is [0–0.02].
Figure 9.
Cross sectional slices of the male (top row) and female (bottom row) phantoms in the three axes.
Figure 9.
Cross sectional slices of the male (top row) and female (bottom row) phantoms in the three axes.
Figure 10.
The reconstruction results of the experiment with second dataset: male phantom: (a) exact male phantom image, (b) with the best hyper-parameters using the proposed Hedge-based approach with the first dataset (), (c) with random hyper-parameters ().
Figure 10.
The reconstruction results of the experiment with second dataset: male phantom: (a) exact male phantom image, (b) with the best hyper-parameters using the proposed Hedge-based approach with the first dataset (), (c) with random hyper-parameters ().
Figure 11.
The reconstruction results of the experiment with third dataset: female phantom: (a) exact female phantom image, (b) with the best hyper-parameters using the proposed Hedge-based approach with the first dataset (), (c) with random hyper-parameters ().
Figure 11.
The reconstruction results of the experiment with third dataset: female phantom: (a) exact female phantom image, (b) with the best hyper-parameters using the proposed Hedge-based approach with the first dataset (), (c) with random hyper-parameters ().
Figure 12.
(a) One projection of the original shape. (b) Reconstruction of a 3D shape.
Figure 12.
(a) One projection of the original shape. (b) Reconstruction of a 3D shape.
Table 1.
Values of each hyper-parameter configuration for this study.
Table 1.
Values of each hyper-parameter configuration for this study.
Hyper-Parameters | Values |
---|
| 0,50,70,100,200,500, |
| 2,,, |
| 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30 |
| 1 |
| 0.99 |
| 0.0212 |
Table 2.
Best hyper-parameter configurations have been found by the Hedge and the cross-validation algorithms.
Table 2.
Best hyper-parameter configurations have been found by the Hedge and the cross-validation algorithms.
Approaches | | | | | |
---|
Hedge-based approach | 0 | 10 | 1 | 0.99 | 0.0212 |
Cross-Validation approach | 0 | 8 | 1 | 0.99 | 0.0212 |
Table 3.
Relative errors, UQI and computational time of image reconstruction results from two hyper-parameter selection approaches. (Boldface numbers indicate the best result).
Table 3.
Relative errors, UQI and computational time of image reconstruction results from two hyper-parameter selection approaches. (Boldface numbers indicate the best result).
Approaches | Relative Errors (%) | UQI | Computational Time |
---|
| | | (h) |
---|
Hedge-based | 4.9349 | 0.9972 | 16.12 |
Cross-validation | 5.2597 | 0.9970 | 47.15 |
Table 4.
The details of anatomical and motion parameters for male and female phantoms.
Table 4.
The details of anatomical and motion parameters for male and female phantoms.
Parametrisation Details | Male Phantom | Female Phantom |
---|
motion option | beating heart only | respiratory only |
length of beating heart cycle | 1 sec | 5 secs |
starting phase of the heart | 0.0 | 0.4 |
wall thickness for the left | | |
ventricle(LV) | non-uniform | uniform |
LV end-systolic volume | 0.0 | 0.5 |
start phase of the respiratory | 0.0 | 0.4 |
anteroposterior diameter | | |
of the ribcage, body and lungs | 0.5 | 1.2 |
heart’s lateral motion | | |
during breathing | 0.0 | 0.5 |
heart’s up/down motion | | |
during breathing | 2.0 | 3.0 |
breast type | prone | supine |
factor to compress breast | half compression | no compression |
thickness of sternum | 0.4 | 0.6 |
thickness of scapula | 0.35 | 0.55 |
thickness of ribs | 0.3 | 0.5 |
thickness of backbone | 0.4 | 0.6 |