CT图像重建滤波器的插值核函数构造法及实例

CT Image Reconstruction Filter Design Method by Interpolation Kernel Functions and Examples

在经典Radon逆变换的基础上,提出了一种实现Radon逆变换的二阶差商反投影(Second-order Divided-difference Back Projection,SDBP)方法.对于离散投影数据,利用插值法将离散的投影值采样序列转化为连续的投影函数,并根据SDBP公式进一步推导出一种基于插值核函数构造的滤波器设计模型.作为该模型的应用,文章套用三角形函数得到了一类新型滤波器.相比传统的滤波器,新型滤波器具有调节性能的可控参数,可以根据实际需求增强某些特性,从而能获得更加理想的重建图像.

Based on the classical inverse Radon transform,the Second-order Divideddifference Back Projection(SDBP)method for realizing inverse Radon transform is proposed in this paper.For discrete projection data,the discrete projection sampling sequence is transformed into continuous projection function by data interpolation.Through logical derivation,a filter design model based on interpolation kernel functions is proposed by using SDBP formula.As an application of the flter design model,a new kind of filter is obtained by applying triangle function.Compared with traditional filters,the new filter has controllable parameters to adjust the performance.Such that some features can be enhanced on the basis of actual needs,so as to obtain better reconstructed images.