ISSN 1004-4140
CN 11-3017/P
| Citation: |
JIANG M, TAO H W, Cheng K. Sparse View CT Reconstruction Algorithm Based on Non-Local Generalized Total Variation Regularization[J]. CT Theory and Applications, 2025, 34(1): 129-139. DOI: 10.15953/j.ctta.2023.170. (in Chinese).
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CT image reconstruction algorithm based on generalized total variation (TGV) can overcome the staircase effect of total variation (TV) regularization, thereby protecting the structural features of the reconstructed image transition region. Although the TGV reconstruction method is superior to the TV reconstruction method, it still ignores the role of non-local self-similar prior information in restoring CT image details. To overcome the aforementioned limitations of TGV reconstruction method, we introduce a non-local TGV (NLTGV) regularization term and propose a sparse view CT reconstruction algorithm based on NLTGV regularization. The proposed method can not only utilize non-local variational information of different orders to protect image structural features but can also utilize non-local self-similarity to restore the details of the reconstructed image. Owing to the inclusion of dual non-smooth terms in the reconstruction model, solving it directly is difficult. Therefore, we proposed an optimization algorithm based on convex set projection, which decomposes the problem into several sub-problems to be solved. The simulation and experimental results show that the proposed NLTGV regularization reconstruction method can effectively improve the quality of reconstructed images compared with other variational reconstruction methods.
| [1] |
PARCERO E, FLORES L, SÁNCHEZ M G, et al. Impact of view reduction in CT on radiation dose for patients[J]. Radiation Physics and Chemistry, 2017, 137(8): 173-175.
|
| [2] |
CANDES E J, ROMBERG J, TAO T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509. DOI: 10.1109/TIT.2005.862083.
|
| [3] |
SIDKY E Y, KAO C M, PAN X. Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT[J]. Journal of X Ray Science & Technology, 2009, 14(2): 119-139.
|
| [4] |
SIDKY E Y, PAN X. Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization[J]. Physics in Medicine & Biology, 2008, 53(17): 4777-4807.
|
| [5] |
RUDIN L I, OSHER S, FATEMI E. Nonlinear total variation based noise removal algorithms[J]. Physica D: Nonlinear Phenomena, 1992, 60(1/4): 259-268.
|
| [6] |
GORDON R, BENDER R, HERMAN G T. Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography[J]. Journal of Theoretical Biology, 1970, 29(3): 471-481. DOI: 10.1016/0022-5193(70)90109-8.
|
| [7] |
LANGE K, CARSON R E. EM reconstruction algorithms for emission and transmission tomography[J]. Journal of Computer Assisted Tomography, 1984, 8(2): 306-316.
|
| [8] |
BREDIES, K, KUNISCH, K, POCK, T. Total genera-lized variation[J]. SIAM Journal on Imaging Sciences, 2010, 3(3): 492-526. DOI: 10.1137/090769521.
|
| [9] |
NIU S, GAO Y, BIAN Z, et al. Sparse-view X-ray CT reconstruction via total generalized variation regularization[J]. Physics in Medicine & Biology, 2014, 59(12): 2997-3017.
|
| [10] |
SUN T, SUN N, WANG J, et al. Iterative CBCT reconstruction using Hessian penalty[J]. Physics in Medicine and Biology, 2015, 60(5): 1965-1987. DOI: 10.1088/0031-9155/60/5/1965.
|
| [11] |
ZHANG H M, WANG L Y, YAN B, et al. Constrained total generalized p-variation minimization for few-view X-ray computed tomography image reconstruction[J]. Plos One, 2016, 11(2): e0149899.
|
| [12] |
XI Y R, QIAO Z R, WANG W J, et al. Study of CT image reconstruction algorithm based on high order total variation[J]. Optik, 2020, 204: 163814. DOI: 10.1016/j.ijleo.2019.163814.
|
| [13] |
闫慧文, 乔志伟. 基于 ASD-POCS 框架的高阶 TpV 图像重建算法[J]. CT 理论与应用研究, 2021, 30(3): 279-289. DOI: 10.15953/j.1004-4140.2021.30.03.01.
YAN H W, QIAO Z W. High order TpV image reconstruction algorithms based on ASD-POCS framework[J]. CT Theory and Applications, 2021, 30(3): 279-289. DOI:10.15953/j.1004-4140.2021.30.03.01. (in Chinese).
|
| [14] |
XI Y, ZHOU P, YU H, et al. Adaptive-weighted high order TV algorithm for sparse-view CT reconstruction[J]. Medical Physics, 2023, 50: 5568-5584. DOI: 10.1002/mp.16371.
|
| [15] |
HUANG J, MA J, LIU N, et al. Sparse angular CT reconstruction using non-local means based iterative-correction POCS[J]. Computers in Biology and Medicine, 2011, 41(4): 195-205. DOI: 10.1016/j.compbiomed.2011.01.009.
|
| [16] |
KIM H, CHEN J, WANG A, et al. Non-local total-variation (NLTV) minimization combined with reweighted L1-norm for compressed sensing CT reconstruction[J]. Physics in Medicine & Biology, 2016, 61(18): 6878.
|
| [17] |
KIM K, EL F G, LI Q. Low-dose CT reconstruction using spatially encoded nonlocal penalty[J]. Physics in Medicine & Biology, 2018, 63(3): 035045.
|
| [18] |
GILBOA G, OSHER S. Nonlocal operators with applications to image processing[J]. Multiscale Modeling & Simulation, 2009, 7(3): 1005-1028.
|
| [19] |
RANFTL R, BREDIES K, POCK T. Non-local total generalized variation for optical flow estimation[C]//ECCV, 2014, (6): 439-454.
|
| [20] |
TOMASI C, MANDUCHI R. Bilateral filtering for gray and color images[C]//ICCV, 1998: 839-846.
|
| [21] |
JIANG M, WANG G. Convergence of the simultaneous algebraic reconstruction technique (SART)[J]. IEEE Transactions on Image Processing, 2003, 12(8): 957-961. DOI: 10.1109/TIP.2003.815295.
|
| [22] |
GOLDSTEIN T, OSHER S. The split Bregman method for L1-regularized problems[J]. SIAM Journal on Imaging Sciences, 2009, 2(2): 323-343. DOI: 10.1137/080725891.
|
| [23] |
WANG Z, BOVIK A C, SHEIKH H R, et al. Image quality assessment: From error visibility to structural similarity[J]. IEEE Transactions on Image Processing, 2004, 13(4): 600-612. DOI: 10.1109/TIP.2003.819861.
|
| [24] |
WANG J, LI T, XING L. Iterative image reconstruction for CBCT using edge-preserving prior[J]. Medical Physics, 2009, 36(1): 252-260. DOI: 10.1118/1.3036112.
|
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