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 引用本文: 康慧, 高红霞, 胡跃明, 郭琪伟. 基于Bregman迭代的CT图像重建算法. 自动化学报, 2013, 39(9): 1570-1575.
KANG Hui, GAO Hong-Xia, HU Yue-Ming, GUO Qi-Wei. Reconstruction Algorithm Based on Bregman Iteration. ACTA AUTOMATICA SINICA, 2013, 39(9): 1570-1575. doi: 10.3724/SP.J.1004.2013.01570
 Citation: KANG Hui, GAO Hong-Xia, HU Yue-Ming, GUO Qi-Wei. Reconstruction Algorithm Based on Bregman Iteration. ACTA AUTOMATICA SINICA, 2013, 39(9): 1570-1575.

Reconstruction Algorithm Based on Bregman Iteration

Funds:

Supported by National High Technology Research and Development Program of China (863 Program) (2012AA041312), National Natural Science Foundation of China (60835001, 61040011), Fundamental Research Funds for the Central Universities (2012ZZ0107), and Strategic Emerging Industry Special Funds of Guangdong Province "LED Industry Project"

• 摘要: 针对大规模集成电路领域CT重建图像的特点,提出TV约束条件下采用l1范数作正则项的重建模型,并给出了基于Bregman迭代的模型求解算法.算法分为两步: 1)采用Bregman迭代求解图像的l1范数作为正则项,误差的加权l2范数作为保真项的约束极值问题;2) 采用TV约束对1)中得到的重建图像进行修正.算法对TV约束条件下采用l1作正则项的重建模型分开求解,降低了算法的复杂度,加快了收敛速度.算法在稀疏投影数据下可以快速重建CT图像且质量较好.本文采用经典的Shepp-Logan图像进行仿真实验并对实际得到的电路板投影数据进行重建,结果表明该算法可满足重建质量要求且重建速度有较大提升.
•  [1] Gordon R, Guan H Q. Computed tomography using algebraic reconstruction techniques (ARTs) with different projection access schemes: a comparison study under practical situations. Physics in Medicine and Biology, 1996, 41(9): 1727-1743 [2] Defrise M, Clack R. A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection. IEEE Transactions on Medical Imaging, 1994, 13(1): 186-195 [3] Anderson A H, Kak A C. Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm. Ultrasonic Imaging, 1984, 6(1): 81-94 [4] Sidky E Y, Kao C M, Pan X C. Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT. Journal of X-Ray Science and Technology, 2006, 14(2): 119-139 [5] Sidky E Y, Pan X C. Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Physics in Medicine and Biology, 2008, 53(17): 4777-4807 [6] Candés E J, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 2006, 52(2): 489-509 [7] Xu J J, Osher S. Iterative regularization and nonlinear inverse scale space applied to wavelet-based denoising. IEEE Transactions on Image Processing, 2007, 16(2): 534-544 [8] Osher S, Burger M, Goldfarb D, Xu J J, Yin W T. An iterative regularization method for total variation-based image restoration. Multiscale Modeling and Simulation, 2005, 4(2): 460-489 [9] Wakin M B, Laska J N, Duarte M F, Baron D, Sarvotham S, Takhar D, Kelly K F, Baraniuk R G. An architecture for compressive imaging. In: Proceedings of the 2006 IEEE International Conference on Image Processing. Atlanta, GA: IEEE, 2006. 1273-1276 [10] Lustig M, Donoho D, Pauly J M. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine, 2007, 58(6): 1182-1195 [11] Candes E J, Tao T. Near-optimal signal recovery from random projections: universal encoding strategies. IEEE Transactions on Information Theory, 2006, 52(12): 5406-5425 [12] Bregman L M. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics, 1967, 7(3): 200-217 [13] Xing Hai-Xia. Image Inpainting Based on Sparse Representation [Master dissertation], Northwest University, China, 2011 (邢海霞. 基于稀疏表示的图像修补研究 [硕士学位论文]. 西北大学, 中国, 2011) [14] Yin W T, Osher S, Goldfarb D, Darbon J. Bregman iterative algorithms for l1-minimization with applications to compressed sensing. SIAM Journal on Imaging Sciences, 2008, 1(1): 143-168 [15] Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4): 586-597 [16] Hale E T, Yin W T, Zhang Y. A Fixed-point Continuation Method for l1-Regularized Minimization with Applications to Compressed Sensing, CAAM Technical Report TR07-07, Rice University, USA, 2007 [17] Wen Z W, Yin W T, Goldfarb D, Zhang Y. A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization, and continuation. SIAM Journal on Scientific Computing, 2010, 32(4): 1832-1857

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出版历程
• 收稿日期:  2012-10-11
• 修回日期:  2013-04-25
• 刊出日期:  2013-09-20

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