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CT (computed tomography)系统实际应用当中, 经常会出现扫描数据不满足数据完备性条件的情况. 针对不完全角度重建问题的研究, 是目前迭代型算法研究中的一个热点. 一系列基于带有约束的总变分最小化的重建算法近年来在不完全角度重建中取得了较好的效果, 这其中基于交替方向法 (alternating direction method, ADM) 的重建算法表现出更好的性能. 然而, ADM方法在求解过程中对矩阵求逆的处理效率不高, 导致极大的计算开销. 本文针对该问题, 使用非精确ADM方法, 利用线性近似的方式替换掉计算开销较大的项, 使得矩阵求逆问题可以通过快速傅里叶变换加速实现. 实验结果表明, 本文提出的非精确交替方向总变分最小化重建算法与精确ADM重建算法相比, 没有明显的精度损失, 计算时间缩减30%左右.Image reconstruction algorithms implemented in existing computed tomography (CT) scanners require that the projection data should be available in proportional-space. The image reconstruction from the projections viewed from few angles has already been one of the hot problems in the research of iterative reconstruction algorithms. Total variation (TV)-based CT image reconstruction has shown to be experimentally capable of producing accurate reconstructions from sparse-view data. Reconstruction algorithms based on alternating direction method (ADM) show higher performance among these TV-based algorithms. However, computing the pseudoinverse at each iteration is too costly to implement numerically in the exact ADM algorithm. For this problem, then inexact ADM is adopted, which uses linearization and proximal points techniques such that computing the pseudoinverse can be accomplished by fast Fourier transforms. Experimental results demonstrate that the proposed method can accelerate the exact ADM algorithm, with little accuracy loss, and the computing time is approximatively reduced by 30%.
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Keywords:
- sparse-view reconstruction /
- total variation minimization /
- inexact alternating direction method
[1] Tuy H 1983 SIAM J. Apply. Math. 43 546
[2] Smith B D 1985 IEEE Trans. Med. Imag. 4 14
[3] Andersen A H 1989 IEEE Trans. Med. Imag. 8 50
[4] Candes E, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489
[5] Candes E, Romberg J, Tao T 2006 Commun. Pure Appl. Math. 59 1207
[6] Sidky E Y, Kao C M, Pan X 2006 J. X-ray Sci. Technol. 14 119
[7] Sidky E Y, Pan X 2008 Phys. Med. Biol. 53 4777
[8] Wang L, Li L, Yan B, Jiang C, Wang H, Bao S 2010 Chin. Phys. B 19 088106
[9] Vandeghinste B, Goossens B, De Beenhouwer J, Pizurica A, Philips W, Vandenberghe S, Staelens S 2011 Proceedings of 11th International Conference on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine, Potsdam, Germany, July 11-15, 2011 p431
[10] Han X, Bian J, Ritman E J, Sidky E Y, Pan X 2012 Phys. Med. Biol. 57 5245
[11] Goldstein T, Osher S 2009 SIAM J. Imag. Sci. 2 323
[12] Li C B 2009 M. S. Thesis (Houston: Rice University, USA)
[13] Osher S, Yin W, Goldfarb D 2008 Siam J. Imag. Sci. 1 143
[14] Esser E 2009 UCLA CAM Tech. Rep. 09-31
[15] Li C, Yin W, Jiang H, Zhang Y 2012 Rice University CAAM Tech. Rep. 12-13
[16] Zhang H, Wang L, Yan B, Li L, Xi X, Lu L 2013 Chin. Phys. B 22 08
[17] Wen Z, Yin W, Liu X, Zhang Y 2012 Operations Research Transaction 16 49 (in Chinese) [文再文, 印卧涛, 刘歆, 张寅 2012 运筹学学报 16 49]
[18] He B, Liao L, Han D, Yang H 2002 Math. Program. 92 103
[19] Xiao Y, Yang J, Yuan X 2012 Inverse Problems and Imaging 6 547
[20] Xiao Y, Song H 2012 J. Math. Imaging Vis. 44 114
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[1] Tuy H 1983 SIAM J. Apply. Math. 43 546
[2] Smith B D 1985 IEEE Trans. Med. Imag. 4 14
[3] Andersen A H 1989 IEEE Trans. Med. Imag. 8 50
[4] Candes E, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489
[5] Candes E, Romberg J, Tao T 2006 Commun. Pure Appl. Math. 59 1207
[6] Sidky E Y, Kao C M, Pan X 2006 J. X-ray Sci. Technol. 14 119
[7] Sidky E Y, Pan X 2008 Phys. Med. Biol. 53 4777
[8] Wang L, Li L, Yan B, Jiang C, Wang H, Bao S 2010 Chin. Phys. B 19 088106
[9] Vandeghinste B, Goossens B, De Beenhouwer J, Pizurica A, Philips W, Vandenberghe S, Staelens S 2011 Proceedings of 11th International Conference on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine, Potsdam, Germany, July 11-15, 2011 p431
[10] Han X, Bian J, Ritman E J, Sidky E Y, Pan X 2012 Phys. Med. Biol. 57 5245
[11] Goldstein T, Osher S 2009 SIAM J. Imag. Sci. 2 323
[12] Li C B 2009 M. S. Thesis (Houston: Rice University, USA)
[13] Osher S, Yin W, Goldfarb D 2008 Siam J. Imag. Sci. 1 143
[14] Esser E 2009 UCLA CAM Tech. Rep. 09-31
[15] Li C, Yin W, Jiang H, Zhang Y 2012 Rice University CAAM Tech. Rep. 12-13
[16] Zhang H, Wang L, Yan B, Li L, Xi X, Lu L 2013 Chin. Phys. B 22 08
[17] Wen Z, Yin W, Liu X, Zhang Y 2012 Operations Research Transaction 16 49 (in Chinese) [文再文, 印卧涛, 刘歆, 张寅 2012 运筹学学报 16 49]
[18] He B, Liao L, Han D, Yang H 2002 Math. Program. 92 103
[19] Xiao Y, Yang J, Yuan X 2012 Inverse Problems and Imaging 6 547
[20] Xiao Y, Song H 2012 J. Math. Imaging Vis. 44 114
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