| Citation: | LIN Luping, WANG Yongge. CT image reconstruction model and algorithm from few views[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(4): 823-830. doi: 10.13700/j.bh.1001-5965.2016.0232(in Chinese)
|
To improve the accuracy and efficiency of few-view computed tomography (CT) image reconstruction, CT image reconstruction is studied from limited view and sparse view, and a novel objective function of total variation norm is proposed. According to the newly-developed objective function, the next iteration is based on the information acquired in the previous one, through which the updated sparse representation model is achieved at each iteration. Additionally, the constrained optimization problem is converted to unconstrained optimization one by adopting the augmented Lagrangian method. Then it can be equally expressed by three sub-problems which can be solved by the alternating minimization scheme. The experimental results using the proposed strategy show that it can attain higher quality CT images which possess integral information, clear detail and high precision. Furthermore, the relative root mean square error can be reduced by 42.1%-98.5% and the streak indicator 42.8%-98.5%, compared with those using Split Bregman-based algorithm.
| [1] |
闫镔, 李磊.CT图像重建算法[M].北京:科学出版社, 2014:97-112.
YAN B, LI L.CT image reconstruction algorithm[M].Beijing:Science Press, 2014:97-112(in Chinese).
|
| [2] |
CANDES E, 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] |
HASHEMI S, BEHESHTI S, GILL P R, et al.Accelerated compressed sensing based CT image reconstruction[J].Computational & Mathematical Methods in Medicine, 2015:16797. http://europepmc.org/articles/PMC4489012
|
| [4] |
TROPP J A, WRIGHT S J.Computational methods for sparse solution of linear inverse problems[J].Proceedings of the IEEE, 2010, 98(6):948-958. doi: 10.1109/JPROC.2010.2044010
|
| [5] |
WANG Y, YANG J, YIN W, et al.A new alternating minimization algorithm for total variation image reconstruction[J].SIAM Journal on Imaging Sciences, 2008, 1(3):248-272. doi: 10.1137/080724265
|
| [6] |
ZHU Z, WAHID K, BABYN P, et al.Improved compressed sensing-based algorithm for sparse-view CT image reconstruction[J].Computational & Mathematical Methods in Medicine, 2013(18):84-104. https://www.researchgate.net/profile/Paul_Babyn/publication/236255367_Improved_Compressed_Sensing-Based_Algorithm_for_Sparse-View_CT_Image_Reconstruction/links/00b7d53aadf055ea90000000.pdf?inViewer=true&pdfJsDownload=true&disableCoverPage=true&origin=publication_detail
|
| [7] |
邓露珍, 冯鹏, 陈绵毅, 等.一种基于Contourlet变换与分裂Bregman方法的CT图像重建算法[J].CT理论与应用研究, 2014, 23(5):751-759. http://www.cnki.com.cn/Article/CJFDTOTAL-CTLL201405004.htm
DENG L Z, FENG P, CHEN M Y, et al.An CT image reconstruction algorithm based on Contourlet transform and Split Bregman methods[J].CT Theory and Application Research, 2014, 23(5):751-759(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-CTLL201405004.htm
|
| [8] |
NIEN H, FESSLER J A.Fast X-ray CT image reconstruction using a linearized augmented Lagrangian method with ordered subsets[J].IEEE Transactions on Medical Imaging, 2014, 34(2):388-399. https://arxiv.org/abs/1402.4381
|
| [9] |
NIEN H, FESSLER J.Relaxed linearized algorithms for faster X-Ray CT image reconstruction[J].IEEE Transactions on Medical Imaging, 2016, 35(4):1090-1098. doi: 10.1109/TMI.2015.2508780
|
| [10] |
ZHANG H, HAN H, LIANG Z R, et al.Extracting information from previous full-dose CT scan for knowledge-based Bayesian reconstruction of current low-dose CT images[J].IEEE Transactions on Medical Imaging, 2016, 35(6):860-870. http://europepmc.org/abstract/MED/26561284
|
| [11] |
CHEN G J, TANG J, LENG S.Prior image constrained compressed sensing (PICCS):A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets[J].Medical Physics, 2008, 35(2):660-663. doi: 10.1118/1.2836423
|
| [12] |
袁亚湘.非线性优化计算方法[M].北京:科学出版社, 2008:158-173.
YUAN Y X.Nonlinear optimization calculating method[M].Beijing:Science Press, 2008:158-173(in Chinese).
|
| [13] |
LI C B.An efficient algorithm for total variation regularization with applications to the single pixel camera and compressed sensing[D].Houston, TX:Rice University, 2009:18-31.
|
| [14] |
XIE S L, GUAN C T, HUANG W M, et al.Fast TV MR image reconstruction using variable splitting and accelerated alternating direction method with adaptive restart[C]//2015 IEEE International Conference.Piscataway, NJ:IEEE Press, 2015:1085-1088.
|
| [15] |
PEACEMAN D W, RACHFORD H H.The numerical solution of parabolic and elliptic differential equations[J].Journal of the Society for Industrial & Applied Mathematics, 2006, 3(1):28-41. doi: 10.1137/0103003
|
| [16] |
BARZILAI J, BORWEIN J M.Two-point step size gradient methods[J].IMA Journal of Numerical Analysis, 1988, 8(1):141-148. doi: 10.1093/imanum/8.1.141
|
| [17] |
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
|
| [18] |
SIDDON R L.Fast calculation of the exact radiological path for a three-dimensional CT array[J].Medical Physics, 1985, 12(2):252-255. doi: 10.1118/1.595715
|
| [19] |
HESTENES M R.Multiplier and gradient methods[J].Journal of Optimization Theory & Applications, 1969, 4(5):303-320. doi: 10.1007/BF00927673
|
Figures(6) / Tables(2)
Copyright © Journal of Beijing University of Aeronautics and Astronautics
Address: Editorial Department of Journal of Beijing University of Aeronautics and Astronautics, 37 Xueyuan Road, Haidian District, Beijing Post Code: 100191 Email: jbuaa@buaa.edu.cn
Supported by:
Beijing Renhe Information Technology Co., Ltd.
DownLoad:
