13 March 2009 Fast implementation of the image reconstruction algorithm OPED
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Proceedings Volume 7258, Medical Imaging 2009: Physics of Medical Imaging; 72585F (2009) https://doi.org/10.1117/12.813855
Event: SPIE Medical Imaging, 2009, Lake Buena Vista (Orlando Area), Florida, United States
OPED is a reconstruction algorithm for Radon data based on orthogonal polynomial expansion on the disk. The algorithm involves a sum of N terms, which is determined by the number of view angles in the data. Evaluating on a rectangular grid of M×M pixels, the algorithm can be implemented with roughly O(N3) evaluations, if we assume M ≈ N, and the constant is rather large. The new implementation uses a particular polar grid, so that the evaluation operation is reduced to 2N3 + O(N2 logN), a reduction of the evaluation time by a factor of more than 20 times. Linear interpolation on triangle is used to reduce our particular polar grid to the rectangular grid. Numerical experiments are presented to demonstrate the results.
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Yuan Xu, Yuan Xu, Oleg Tischenko, Oleg Tischenko, Christoph Hoeschen, Christoph Hoeschen, } "Fast implementation of the image reconstruction algorithm OPED", Proc. SPIE 7258, Medical Imaging 2009: Physics of Medical Imaging, 72585F (13 March 2009); doi: 10.1117/12.813855; https://doi.org/10.1117/12.813855

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