System matrix analysis for computed tomography imaging

In practical applications of computed tomography imaging (CT), it is often the case that the set of projection data is incomplete owing to the physical conditions of the data acquisition process. On the other hand, the high radiation dose imposed on patients is also undesired. These issues demand that high quality CT images can be reconstructed from limited projection data. For this reason, iterative methods of image reconstruction have become a topic of increased research interest. Several algorithms have been proposed for few-view CT. We consider that the accurate solution of the reconstruction problem also depends on the system matrix that simulates the scanning process. In this work, we analyze the application of the Siddon method to generate elements of the matrix and we present results based on real projection data.This work has been supported by Universitat Politecnica de Valencia and partially funded by ANITRAN PROMETEOII/2014/008 of the Generalitat Valenciana of Spain.Flores, LA.; Vicent Vidal; Verdú Martín, GJ. (2015). System matrix analysis for computed tomography imaging. PLoS ONE. 10(11):1-12. https://doi.org/10.1371/journal.pone.01432021121011Herman, G. T. (2009). Fundamentals of Computerized Tomography. Advances in Pattern Recognition. doi:10.1007/978-1-84628-723-7Wang, G., Yu, H., & De Man, B. (2008). An outlook on x-ray CT research and development. Medical Physics, 35(3), 1051-1064. doi:10.1118/1.2836950Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289-1306. doi:10.1109/tit.2006.871582Candès, E. J., Romberg, J. K., & Tao, T. (2006). Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure and Applied Mathematics, 59(8), 1207-1223. doi:10.1002/cpa.20124Yu, H., & Wang, G. (2010). A soft-threshold filtering approach for reconstruction from a limited number of projections. Physics in Medicine and Biology, 55(13), 3905-3916. doi:10.1088/0031-9155/55/13/022Andersen, A. H., & Kak, A. C. (1984). Simultaneous Algebraic Reconstruction Technique (SART): A Superior Implementation of the Art Algorithm. Ultrasonic Imaging, 6(1), 81-94. doi:10.1177/016173468400600107Flores, L. A., Vidal, V., Mayo, P., Rodenas, F., & Verdú, G. (2013). CT Image Reconstruction Based on GPUs. Procedia Computer Science, 18, 1412-1420. doi:10.1016/j.procs.2013.05.308Flores, L., Vidal, V., & Verdú, G. (2015). Iterative Reconstruction from Few-view Projections. Procedia Computer Science, 51, 703-712. doi:10.1016/j.procs.2015.05.188Cibeles Mora Mora, T. Métodos de reconstrucción volumétrica algebraica de imágenes tomográficas. 2008. Tesis PhD. Spain.Siddon, R. L. (1985). Fast calculation of the exact radiological path for a three-dimensional CT array. Medical Physics, 12(2), 252-255. doi:10.1118/1.595715Joseph, P. M. (1982). An Improved Algorithm for Reprojecting Rays through Pixel Images. IEEE Transactions on Medical Imaging, 1(3), 192-196. doi:10.1109/tmi.1982.4307572Paige, C. C., & Saunders, M. A. (1982). LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares. ACM Transactions on Mathematical Software, 8(1), 43-71. doi:10.1145/355984.355989Higham, N. J. (1993). The Accuracy of Floating Point Summation. SIAM Journal on Scientific Computing, 14(4), 783-799. doi:10.1137/091405