Abstract
Sparse angle projection CT image reconstruction in medical diagnosis and industrial non-destructive testing has important theoretical significance and practical application value. In the paper, L1 norm was introduced as the CT images of regular constraint and optimization reconstruction model, and the method to solve it was presented based on the Split Bregman algorithm. Shepp-Logan numerical simulation experiments show that the image reconstructed by the traditional algebraic reconstruction algorithm of ART for sparse projection CT is poor. The Split Bregman may solve L1 regularization constraint model of sparse projection of CT with less number of iterations, fast reconstruction and good reconstruction quality. For the splitting factor of the algorithm, in a numerical range, the greater the reconstruction quality is better.
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References
Sidky EY, Kao CM, Pan X (2006) Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT. J X-ray Sci Technol 14:119–139
Sidky EY, Pan X (2008) Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization. Phys Med Biol 53:4777–5807
Tuy HK (1983) An inversion formula for cone-beam reconstruction. SIAM J Appl Math 43(3):542–546
Smith BD (1985) Image reconstruction from cone-beam projections:necessary and sufficient conditions and reconstruction methods. IEEE Trans Med Imag 4(1)
Gordon R (1974) A tutorial on ART (algebraic reconstruction techniques). IEEE Trans Nucl Sci 21(3):78–93
Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306
Bregman LM (1967) The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput Math Math Phys 7:200–217
Goldstein T, Osher S (2009) The split Bregman method for L1-regularized problems. SIAM J Imag Sci 2(2):323–343
Avinash CK, Slaney M (2001) Principles of Computerized Tomographic Imaging. Society for Industrial and Applied Mathematics, Philadelphia
Wang Y, Yin W, Zhang Y (2007) A fast algorithm for image deblurring with total variation regularization. CAAM Technical Reports (2007)
Acknowledgments
This research are financially supported by the Science and Technology Plan Projects of Lanzhou city, P. R. China (Grant No.214160) and the Youth Science Fund of Lanzhou Jiaotong University, P. R. China (Grant No.2012035).
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Gou, Jn., Dong, Hy. (2017). Sparse Projection CT Image Reconstruction Based on the Split Bregman Less Iteration. In: Balas, V., Jain, L., Zhao, X. (eds) Information Technology and Intelligent Transportation Systems. Advances in Intelligent Systems and Computing, vol 455. Springer, Cham. https://doi.org/10.1007/978-3-319-38771-0_21
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DOI: https://doi.org/10.1007/978-3-319-38771-0_21
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