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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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