CT图像重建中滤波函数的优化

Optimization of Filter Function in CT Image Reconstruction

CT图像重建的解析类经典算法为滤波反投影(FBP),其中的滤波环节对于重建质量的影响至关重要,通常情况下滤波函数都是将斜坡函数直接加矩形窗,而理想的矩形窗是造成Gibbs现象的根源所在,Gibbs现象使重建图像出现震荡,不够平滑。根据无穷级数求和理论,将函数展开成级数部分和形式后,可以进一步求解出部分和的算术平均值,该函数即是具有更优收敛性的费耶核(Fejes),本文根据这一理论,提出了一种改进的滤波方法,尝试利用费耶核较好的收敛性来克服Gibbs现象。实验结果表明该方法可以获得更加平滑的结果,对于图像质量的改善取得了明显的效果。

FBP is the most popular analytical algorithm used to reconstruct image in CT system. The filtering process before back projection plays an important role relate to the image reconstruction quality. Usually the filtering function is acquired by Ramp function multiplying a rectangular window; however the ideal rectangular window will lead to a rough reconstruction result because of Gibbs artifact. According to the theory of infinite series, the arithmetic average named Fejer-core can be abstained after the function is expanded to the form of part sum. The core function has superiority convergence property. So to avoid Gibbs phenomena, the paper advances an improvement filtering method .Experiment result shows that Gibbs is avoided when convolve the filtered projections with Fejer-core. So smooth image can be obtained.