TY - JOUR
T1 - Structure tensor total variation for CBCT reconstruction
AU - Tan, Xi
AU - Xiang, Kai
AU - Liu, Liang
AU - Wang, Jing
AU - Tan, Shan
N1 - Funding Information:
This work was supported in part by National Natural Science Foundation of China (NNSFC), under Grant Nos. 61375018 and 61672253. J. Wang was supported in part by grants from the Cancer Prevention and Research Institute of Texas (RP160661) and the National Institute of Biomedical Imaging and Bioengineering (R01 EB020366).
PY - 2019
Y1 - 2019
N2 - The total variation (TV) regularization has been widely used in statistically iterative cone-beam computed tomography (CBCT) reconstruction, showing ability to preserve object edges. However, the TV regularization can also produce staircase effect and tend to over-smooth the reconstructed images due to its piecewise constant assumption. In this study, we proposed to use the structure tensor total variation (STV) that penalizes the eigenvalues of the structure tensor for CBCT reconstruction. The STV penalty extends the TV penalty, with many important properties maintained such as convexity and rotation and translation invariance. The STV penalty utilizes gradient information more effectively and has a stronger ability to capture local image structural variation. The objective function was constructed with the penalized weighted least-square (PWLS) strategy and the gradient descent (GD) method was used to optimize the objective function. Besides, we investigated whether the norms involved in the STV penalty affected the reconstruction performance and found that the l1-norm gave the better performance than the l2-norm and l8-norm. We also examined performance of the STV penalties constructed using different kernel functions and found that the STV with the Gaussian kernel had the best performance, and the STVs with Uniform, Logistic, and Sigmoid kernels had similar performance to each other. We evaluated our reconstruction method with the STV penalty on computer simulated phantoms and physical phantoms. The results demonstrated that STV led to better reconstruction performance than TV, both visually and quantitatively. For the Catphan 600 physical phantom, the STV1 penalty was 175% and 623% better than the low-dose FDK and the high-dose FDK, and 14% better than the TV penalty at the matched noise level, according to the average contrast-to-noise ratio (CNR); while for the Compressed Sensing simulation phantom, the peak signal to noise ratio (PSNR) of reconstructed results using STV1, STV2, and STV8 were 40.67 dB, 38.72 dB, and 37.40 dB, respectively, all being significantly better than 36.84 dB using TV.
AB - The total variation (TV) regularization has been widely used in statistically iterative cone-beam computed tomography (CBCT) reconstruction, showing ability to preserve object edges. However, the TV regularization can also produce staircase effect and tend to over-smooth the reconstructed images due to its piecewise constant assumption. In this study, we proposed to use the structure tensor total variation (STV) that penalizes the eigenvalues of the structure tensor for CBCT reconstruction. The STV penalty extends the TV penalty, with many important properties maintained such as convexity and rotation and translation invariance. The STV penalty utilizes gradient information more effectively and has a stronger ability to capture local image structural variation. The objective function was constructed with the penalized weighted least-square (PWLS) strategy and the gradient descent (GD) method was used to optimize the objective function. Besides, we investigated whether the norms involved in the STV penalty affected the reconstruction performance and found that the l1-norm gave the better performance than the l2-norm and l8-norm. We also examined performance of the STV penalties constructed using different kernel functions and found that the STV with the Gaussian kernel had the best performance, and the STVs with Uniform, Logistic, and Sigmoid kernels had similar performance to each other. We evaluated our reconstruction method with the STV penalty on computer simulated phantoms and physical phantoms. The results demonstrated that STV led to better reconstruction performance than TV, both visually and quantitatively. For the Catphan 600 physical phantom, the STV1 penalty was 175% and 623% better than the low-dose FDK and the high-dose FDK, and 14% better than the TV penalty at the matched noise level, according to the average contrast-to-noise ratio (CNR); while for the Compressed Sensing simulation phantom, the peak signal to noise ratio (PSNR) of reconstructed results using STV1, STV2, and STV8 were 40.67 dB, 38.72 dB, and 37.40 dB, respectively, all being significantly better than 36.84 dB using TV.
KW - CBCT
KW - Image reconstruction
KW - Staircase effect
KW - Structure tensor
KW - Total variation
UR - http://www.scopus.com/inward/record.url?scp=85065213492&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85065213492&partnerID=8YFLogxK
U2 - 10.3233/XST-180419
DO - 10.3233/XST-180419
M3 - Article
C2 - 30741716
AN - SCOPUS:85065213492
SN - 0895-3996
VL - 27
SP - 257
EP - 272
JO - Journal of X-Ray Science and Technology
JF - Journal of X-Ray Science and Technology
IS - 2
ER -