Low Dose CT Image Reconstruction Based on Structure Tensor Total Variation Using Accelerated Fast Iterative Shrinkage Thresholding Algorithm
Abstract
:1. Introduction
2. Materials and Methods
2.1. SIR
2.2. SIR with STV1 Penalty for Low Dose CT Reconstruction
2.3. AFISTA Algorithm for Solving SIR-STV1
2.3.1. General FISTA for Solving SIR-STV1
Algorithm 1 Workflow of the general fast iterative shrinkage thresholding algorithm (FISTA). |
Input: system matrix , projection data , Q is the Lipschitz constant of |
Initial Step:, , maximum iteration number I, regularization parameter , convolution kernel |
fori = 1,2,...,I |
Update intermediate image with (7) |
Update image with (8) |
end for |
output: |
2.3.2. AFISTA for Solving SIR-STV1
Algorithm 2 Workflow of the progressive proximal map algorithm |
Input:, , |
Initial Step:, |
fori = 1,2,...,I |
end for |
Output |
Algorithm 3 Workflow of the proposed accelerated (A)FISTA |
Input: System matrix , projection data , , , |
Initial Step:, , maximum iteration number I, regularization parameter , convolution kernel K, the number of order subset M |
fori = 1,2...I |
for m = 1,...M |
Update intermediate image using Equation (10): |
, , are submatrices of , , corresponding to the mth subset |
Update image with progressive proximal map algorithm using Algorithm 2 |
end for |
end for |
Output |
3. Experimental Results
3.1. Brain Image Numerical Simulation
3.1.1. Convergence Analysis
3.1.2. Visual Quality Comparison
3.1.3. Quantitative Comparison
3.2. Thorax Image Numerical Simulation
3.2.1. Visual Quality Comparison
3.2.2. Quantitative Comparison
3.2.3. Profile-Based Comparison
3.2.4. Analysis of the Parameter
3.3. Realistic Sheep Lung Experiments
4. Discussion and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Incident Photon Number | Algorithm | PSNR (dB) | RRE | SSIM |
---|---|---|---|---|
5 × 103 | FBP | 26.6131 | 0.2049 | 0.5526 |
SIR-TV | 33.8416 | 0.0892 | 0.7539 | |
SIR-STV1 | 35.7597 | 0.0715 | 0.7639 | |
1 × 104 | FBP | 29.8176 | 0.1417 | 0.6135 |
SIR-TV | 35.7454 | 0.0716 | 0.8162 | |
SIR-STV1 | 38.2683 | 0.0536 | 0.8248 | |
5 × 104 | FBP | 36.7103 | 0.0641 | 0.7318 |
SIR-TV | 40.2409 | 0.0427 | 0.9016 | |
SIR-STV1 | 42.8079 | 0.0307 | 0.9275 |
Different ROI | Algorithm | PSNR (dB) | RRE | SSIM |
---|---|---|---|---|
ROI 1 | FBP | 30.7537 | 0. 0447 | 0.7403 |
SIR-TV | 35.0948 | 0.0271 | 0.9206 | |
SIR-STV1 | 35.7648 | 0.0251 | 0.9370 | |
ROI 2 | FBP | 29.9316 | 0.0540 | 0.7730 |
SIR-TV | 33.1043 | 0.0374 | 0.9145 | |
SIR-STV1 | 34.2960 | 0.0326 | 0.9348 | |
ROI 3 | FBP | 30.0721 | 0.0446 | 0.7021 |
SIR-TV | 33.8564 | 0.0288 | 0.8927 | |
SIR-STV1 | 34.9798 | 0.0253 | 0.9183 |
Parameter | PSNR (dB) | RRE | SSIM |
---|---|---|---|
, LK = 3 | 37.7983 | 0.0290 | 0.9449 |
, LK = 5 | 37.9762 | 0.0283 | 0.9477 |
, LK = 7 | 37.9653 | 0.0284 | 0.9482 |
, LK = 9 | 37.8765 | 0.0287 | 0.9480 |
, LK = 11 | 37.7748 | 0.0291 | 0.9474 |
, LK = 13 | 37.6704 | 0.0294 | 0.9466 |
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Wu, J.; Wang, X.; Mou, X.; Chen, Y.; Liu, S. Low Dose CT Image Reconstruction Based on Structure Tensor Total Variation Using Accelerated Fast Iterative Shrinkage Thresholding Algorithm. Sensors 2020, 20, 1647. https://doi.org/10.3390/s20061647
Wu J, Wang X, Mou X, Chen Y, Liu S. Low Dose CT Image Reconstruction Based on Structure Tensor Total Variation Using Accelerated Fast Iterative Shrinkage Thresholding Algorithm. Sensors. 2020; 20(6):1647. https://doi.org/10.3390/s20061647
Chicago/Turabian StyleWu, Junfeng, Xiaofeng Wang, Xuanqin Mou, Yang Chen, and Shuguang Liu. 2020. "Low Dose CT Image Reconstruction Based on Structure Tensor Total Variation Using Accelerated Fast Iterative Shrinkage Thresholding Algorithm" Sensors 20, no. 6: 1647. https://doi.org/10.3390/s20061647