ISSN 1004-4140
CN 11-3017/P
Volume 31 Issue 6
Nov.  2022
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MA J Y, QIAO Z W. Nuclear TV multi-channel image reconstruction algorithms based on Chambolle-pock framework[J]. CT Theory and Applications, 2022, 31(6): 731-747. DOI: 10.15953/j.ctta.2022.111. (in Chinese).
Citation: MA J Y, QIAO Z W. Nuclear TV multi-channel image reconstruction algorithms based on Chambolle-pock framework[J]. CT Theory and Applications, 2022, 31(6): 731-747. DOI: 10.15953/j.ctta.2022.111. (in Chinese).
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Nuclear TV Multi-channel Image Reconstruction Algorithm Based on Chambolle-pock Framework

  • School of Computer and Information Technology, Shanxi University, Taiyuan 030006, China

More Information
  • Received Date: June 07, 2022
  • Revised Date: June 27, 2022
  • Accepted Date: June 28, 2022
  • Available Online: July 17, 2022
  • Published Date: November 02, 2022
    Graphical Abstract
    • Abstract
  • Total variation (TV) minimum algorithm is an image reconstruction algorithm based on compressed sensing theory, which can realize the reconstruction of images with high accuracy from sparse projection or noisy projection data and has been widely used in computed tomography (CT), magnetic resonance imaging (MRI) and electronic paramagnetic resonance imaging (EPRI). Energy spectrum CT, T1 or T2 weighted MRI and EPRI both belong to multi-channel imaging. The channel-by-channel TV algorithm can achieve high-precision image reconstruction, but it ignores the similarity among the images of each channel while Nuclear TV algorithm is a TV algorithm that considers the image similarity among channels, and can realize high-precision image reconstruction. For multi-channel image reconstruction, taking CT reconstruction as an example, this paper proposes a nuclear TV multi-channel image reconstruction algorithm based on the framework of Chambolle-pock algorithm. Through the reconstruction experiments of simulated phantom and real CT image phantom, the accuracy of the algorithm is verified, the convergence of the algorithm is analyzed, the influence of algorithm parameters on the convergence rate is explored, and the sparse reconstruction ability and noisy projection reconstruction ability of the algorithm are evaluated. The experimental results show that the proposed algorithm can achieve higher reconstruction accuracy than the channel-by-channel TV algorithm. Nuclear TV algorithm is a high-precision multi-channel image reconstruction algorithm, which can be applied to multi-channel reconstruction of various imaging modes.
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    • References (26)
  • [1]
    PAN X C, SIDKY E Y, VANNIER M. Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?[J]. Inverse Problems, 2008, 25(12): 1230009.
    [2]
    YU L, YU Z, SIDKY E Y, et al. Region of interest reconstruction from truncated data in circular cone-beam CT[J]. IEEE Transactions on Medical Imaging, 2006, 25(7): 869−881. doi: 10.1109/TMI.2006.872329
    [3]
    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
    [4]
    SIDKE E Y, KAO C M, PAN X C. Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT[J]. Journal of X-ray Science & Technology, 2006, 14: 119−139.
    [5]
    PAPAFITSOROS K, SCHOENLIEB C B, SENGUL B. Combined first and second order total variation inpainting using split bregman[J]. Image Processing on Line, 2013, 3: 112−136. doi: 10.5201/ipol.2013.40
    [6]
    XI Y R, QIAO Z W, WANG W J, et al. Study of CT image reconstruction algorithm based on high order total variation - ScienceDirect[J]. Optik, 2020, 204: 163814−163814. doi: 10.1016/j.ijleo.2019.163814
    [7]
    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 algorithm 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).
    [8]
    NING F L, HE B J, WEI J. An algorithm for image reconstruction based on lp norm[J]. Acta Physica Sinica, 2013, 62: 174212−174212. doi: 10.7498/aps.62.174212
    [9]
    张海娇, 孔慧华, 孙永刚. 基于结构先验的加权NLTV能谱CT重建算法[J]. 光学学报, 2018,38(8): 334−342.

    ZHANG H J, KONG H H, SUN Y G. Weighted NLTV energy spectrum CT reconstruction algorithm based on structure prior[J]. Acta Optica Sinica, 2018, 38(8): 334−342. (in Chinese).
    [10]
    DURAN J, MOELLER M, SBERT C, et al. Collaborative total variation: A general framework for vectorial TV models[J]. SIAM Journal on Imaging Sciences, 2015, 9(1): 116−151.
    [11]
    RIGIE D S, RIVIèRE P J L. Joint reconstruction of multi-channel, spectral CT data via constrained total nuclear variation minimization[J]. Physics in Medicine & Biology, 2015, 60(5): 1741−1762.
    [12]
    RIGIE D S, SANCHEZ A A, RIVIèRE P J L. Assessment of vectorial total variation penalties on realistic dual-energy CT data[J]. Physics in Medicine & Biology, 2017, 62(8): 3284−3298.
    [13]
    QIAO Z W. A simple and fast ASD-POCS algorithm for image reconstruction[J]. Journal of X-ray Science and Technology, 2021, 29(3): 1−16.
    [14]
    SIDKY E Y, PAN X C. Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization[J]. Physics in Medicine & Biology, 2008, 53(17): 4777−4807.
    [15]
    CHAMBOLLE A, POCK T. A first-order primal-dual algorithm for convex problems with applications to imaging[J]. Journal of Mathematical Imaging and Vision, 2011, 40(1): 120−145. doi: 10.1007/s10851-010-0251-1
    [16]
    SIDKY E Y, J∅RGENSEN J H, PAN X C. Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm[J]. Physics in Medicine & Biology, 2011, 57(10): 3065−3091.
    [17]
    QIAO Z W, REDLER G, EPEL B, et al. A balanced total-variation-Chambolle-Pock algorithm for EPR imaging[J]. Journal of Magnetic Resonance, 2021, 328: 107009. doi: 10.1016/j.jmr.2021.107009
    [18]
    CAI J, CAND E J, SHEN Z. A singular value thresholding algorithm for matrix completion[J]. SIAM Journal on Optimization, 2010.
    [19]
    DUAN Y H, WEN R P, XIAO Y. A singular value thresholding with diagonal-update algorithm for low-rank matrix completion[J]. Mathematical Problems in Engineering, 2020: 2020.
    [20]
    LI W, HU J, CHEN C. On accelerated singular value thresholding algorithm for matrix completion[J]. Applied Mathematics, 2014, 5(21): 3445−3451. doi: 10.4236/am.2014.521322
    [21]
    QIAO Z W, ZHANG Z, PAN X C, et al. Optimization-based image reconstruction from sparsely sampled data in electron paramagnetic resonance imaging[J]. Journal of Magnetic Resonance, 2018, 294: 24−34. doi: 10.1016/j.jmr.2018.06.015
    [22]
    QIAO Z W, ZHU Y N, REDLER G, et al. The integrated acceleration of the Chambolle-Pock algorithm applied to constrained TV minimization in CT image reconstruction[J]. Inverse Problems in Science and Engineering, 2019.
    [23]
    乔志伟. 总变差约束的数据分离最小图像重建模型及其Chambolle-Pock求解算法[J]. 物理学报, 2018,67(19): 198701. DOI: 10.7498/aps.67.20180839.

    QIAO Z W. Total variation constrained data separation minimum image reconstruction model and its Chambolle-Pock algorithm[J]. Acta Physica Sinica, 2018, 67(19): 198701. DOI: 10.7498/aps.67.20180839. (in Chinese).
    [24]
    QIAO Z W, REDLER G, GUI Z G, et al. Three novel accurate pixel-driven projection methods for 2D CT and 3D EPR imaging[J]. Journal of X-ray Science and Technology, 2018, 26(1): 83−102. doi: 10.3233/XST-17284
    [25]
    QIAO Z W, REDLER G, EPEL B, et al. A doubly constrained TV algorithm for image reconstruction[J]. Mathematical Problems in Engineering, 2020, (2): 1−15.
    [26]
    QIAO Z W, REDLER G, TANG S J, et al. Comparison of TVcDM and DDcTV algorithms in image reconstruction[J]. Inverse Problems in Science and Engineering, 2020, 28(6): 839−858. doi: 10.1080/17415977.2019.1667343
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