Fast implementation of the image reconstruction algorithm OPED

Yuan Xu; Oleg Tischenko; Christoph Hoeschen

doi:10.1117/12.813855

13 March 2009 Fast implementation of the image reconstruction algorithm OPED

Yuan Xu, Oleg Tischenko, Christoph Hoeschen

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

Abstract

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.

Citation Download Citation

Yuan Xu, Oleg Tischenko, and Christoph Hoeschen "Fast implementation of the image reconstruction algorithm OPED", Proc. SPIE 7258, Medical Imaging 2009: Physics of Medical Imaging, 72585F (13 March 2009); https://doi.org/10.1117/12.813855

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