In practical engineering applications, the projection data contains a lot of noise. The Katsevich algorithm is an exact imaging algorithm with good reconstruction image. This algorithm needs derivation operation on projection data rota?tion angle and two-dimensional coordinates of the detector. The derivation will amplify the noise and distort the recon?struction image. Combined with the avoid derivation of the rotation angle and the use of five-point differential method in?stead of direct derivation to the detector coordinate, this algorithm can reduce the sampling rate of rotation angle and the radiation to the patient and X-ray cost. It can lessen the error of the derivative and the negative impact caused by the noise. Thus, it improves the image quality.%在实际工程应用中,投影体数据含有大量噪声. Katsevich算法作为一种精确的重建算法,它可以得到质量较高的重建图像,但它需要对投影数据旋转角和二维探测器坐标做求导运算,求导会放大噪声,甚至使重建图像失真.结合Katsevich算法中对投影数据的旋转角避开求导和探测器坐标求导采用五点差分方法代替直接求导,可以降低对旋转角度的采样率,减少对病人的射线辐射和射线成本,减小求导误差和噪声带来的负面影响,从而提高图像质量.
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