The distance between source and object center | |
The angle interval of two adjacent projection views | |
The angle interval of two adjacent rays | |
The diameter of field of view | |
Detector numbers | |
Pixel size | |
Image size | |
The limited-angle projection data of an object, in some practical applications of computed tomography (CT), are obtained due to the restriction of scanning condition. In these situations, since the projection data are incomplete, some limited-angle artifacts will be presented near the edges of reconstructed image using some classical reconstruction algorithms, such as filtered backprojection (FBP). The reconstructed image can be fine approximated by sparse coefficients under a proper wavelet tight frame, and the quality of reconstructed image can be improved by an available prior image. To deal with limited-angle CT reconstruction problem, we propose a minimization model that is based on wavelet tight frame and a prior image, and perform this minimization problem efficiently by iteratively minimizing separately. Moreover, we show that each bounded sequence, which is generated by our method, converges to a critical or a stationary point. The experimental results indicate that our algorithm can efficiently suppress artifacts and noise and preserve the edges of reconstructed image, what's more, the introduced prior image will not miss the important information that is not included in the prior image.
Citation: |
Figure 4. The wavelet transform of (a) of Figure 3 under B-spline frame
Figure 5. The wavelet transform of (b) of Figure 3 under B-spline frame
Figure 16. The zoom-in view of ROI of Figure 15
Table 1. Geometrical scanning parameters of simulated CT system
The distance between source and object center | |
The angle interval of two adjacent projection views | |
The angle interval of two adjacent rays | |
The diameter of field of view | |
Detector numbers | |
Pixel size | |
Image size | |
Table 2. Quantitatively characterize the reconstruction quality
Scanning ranges | Variances | Algorithm | RMSE | PSNR | MSSIM |
| | FBP | 8.403 | 29.64 | 0.9921 |
| FBP | 12.88 | 25.93 | 0.9800 | |
| our algorithm | 2.116 | 41.62 | 0.9995 | |
PICCS | 3.743 | 36.67 | 0.9985 | ||
| our algorithm | 4.747 | 34.60 | 0.9973 | |
PICCS | 5.953 | 32.64 | 0.9953 | ||
| | our algorithm | 2.240 | 41.12 | 0.9994 |
PICCS | 4.087 | 35.90 | 0.9984 | ||
| our algorithm | 4.258 | 35.55 | 0.9978 | |
PICCS | 4.915 | 32.69 | 0.9953 | ||
| | our algorithm | 1.843 | 42.82 | 0.9996 |
PICCS | 5.905 | 32.71 | 0.9956 | ||
| our algorithm | 3.566 | 37.09 | 0.9985 | |
PICCS | 6.250 | 32.21 | 0.9952 |
Table 3. Geometrical scanning parameters of simulated CT system
The distance between source and object center | |
The angle interval of two adjacent projection views | |
The angle interval of two adjacent rays | |
The diameter of field of view | |
Detector numbers | |
Pixel size | |
Image size | |
Table 4. Quantitatively characterize the reconstruction quality
Scanning ranges | Algorithm | RMSE | PSNR | MSSIM |
| FBP | 4.978 | 34.19 | 0.9961 |
| our algorithm | 3.607 | 36.99 | 0.9979 |
PICCS | 4.208 | 35.65 | 0.9972 | |
| our algorithm | 3.901 | 36.31 | 0.9976 |
PICCS | 4.190 | 35.69 | 0.9972 | |
| our algorithm | 3.693 | 36.78 | 0.9979 |
PICCS | 4.177 | 35.71 | 0.9972 |
Table 5. The parameters of simulated phantom
| | | | | |
1 | 0.74 | 0.74 | 0 | 0 | 0 |
-1 | 0.5 | 0.5 | 0 | 0 | 0 |
-1 | 0.1 | 0.1 | 0.43 | 0.43 | 0 |
-1 | 0.1 | 0.1 | -0.43 | -0.43 | 0 |
-1 | 0.1 | 0.1 | -0.43 | 0.43 | 0 |
-1 | 0.1 | 0.1 | 0.43 | -0.43 | 0 |
-1 | 0.12 | 0.006 | 0.25 | 0.55 | -18 |
-1 | 0.08 | 0.006 | 0.25 | -0.55 | -240 |
-1 | 0.08 | 0.006 | -0.55 | 0.3 | 20 |
Table 6. Quantitatively characterize the reconstruction quality
Scanning ranges | Algorithm | RMSE | PSNR | MSSIM |
| our algorithm | 0.040 | 27.97 | 0.9949 |
PICCS | 0.057 | 28.26 | 0.9897 | |
| our algorithm | 0.0378 | 28.45 | 0.9954 |
PICCS | 0.0546 | 28.65 | 0.9906 |
Table 7. Quantitatively characterize the reconstruction quality
Scanning ranges | Algorithm | RMSE | PSNR | MSSIM |
| 3.725 | 36.71 | 0.9978 | |
| 3.607 | 36.99 | 0.9979 | |
| 3.856 | 36.41 | 0.9977 | |
| 3.901 | 36.31 | 0.9976 |
Table 8. Quantitatively characterize the reconstruction quality
Scanning ranges | Algorithm | RMSE | PSNR | MSSIM |
| 0.0404 | 27.86 | 0.9948 | |
| 0.0400 | 27.97 | 0.9949 | |
| 0.0383 | 28.34 | 0.9954 | |
| 0.0378 | 28.45 | 0.9954 |
Table 9. Quantitatively characterize the reconstruction quality
Scanning ranges | Algorithm | RMSE | PSNR | MSSIM |
| FBP | 6.559 | 31.79 | 0.9965 |
| our algorithm | 4.543 | 34.98 | 0.9983 |
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