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3 March 2012 Analytical fan-beam reconstruction algorithm for free-form trajectory with plus-minus weighting scheme
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This paper focuses on fan-beam image reconstruction from free-form X-ray source trajectory in computed tomography (CT). As in major standard image reconstruction methods, the weighting function of the redundant projection data should be carefully considered. The data redundancy reduction principle aims to compute the projection data only one time during image reconstruction. Usually, an X-ray line that passes through the object point intersects with the radiation source trajectory more than once time. For the symmetric closed circular trajectory, because each X-ray line passing through an object point would intersect with the source trajectory twice, the weighting function of 0.5 is used to handle this problem. However, normally there is no known symmetry property for the free-form X-ray source trajectory. In order to estimate the weighting function we have to calculate the number N of intersection between each X-ray line and every object points, then the weighting function is set to be 1/N such that the summation of weighting operator corresponding to a single X-ray line is the unity. However, the calculation of N is difficult and computationally expensive. In this paper we proposed a new scheme for a robust control of the redundant projection data for both closed and open trajectories. Instead of calculation of N, we assign each intersection point a plus or minus sign according to the proposed weighting function. As a result of summation of successive signs, they cancel out each other and finally equal to the unity. Numerical study was performed to evaluate the proposed weighting scheme using standard Shepp-Logan phantom with butterfly trajectory.
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Zhen Wang, Essam A. Rashed, and Hiroyuki Kudo "Analytical fan-beam reconstruction algorithm for free-form trajectory with plus-minus weighting scheme", Proc. SPIE 8313, Medical Imaging 2012: Physics of Medical Imaging, 83133C (3 March 2012);

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