基于FHT和MSBP的CT图像滤波反投影重建方法设计

Design and realization of filtered backprojection algorithms of CT image reconstruction based on FHT and MSBP

滤波反投影算法(FBP)是商用CT系统中广泛使用的图像重建方法。在CT图像重建应用的场合,投影数据和目标函数都属于实数空间范畴。基于Fourier变换的重建方法涉及大量复数运算,是其在计算上的一个固有特点。与Fourier变换相比,Hartley变换以其实值变换的特点,在实数域能够替代Fourier变换,进行信号和图像的处理。MSBP方法是基于重建图像像素和投影射线之间在不同的投影方位上所存在的几何关系而提出的。将快速Hartley变换(FHT)算法和MSBP方法应用于CT图像的滤波反投影重建方法中,在保持精度不变的前提下,减少了所需的存储空间和计算量。

Filtered backprojection algorithms are widely used in the commercial CT systems. The projection data and the object functions all belong to the real number area in applications of CT image reconstruction. The reconstruction algorithm based on Fourier transform involves lots of complex number operations. Itls an inherent characteristic in computation. Because of the real number transform characteristic of Hartley transform comparing with Fourier transform, the signals and images in the real number area can be processed using Hartley transform instead of Fourier transform. Based on the geometrical relationships between image pixels and projection rays at different viewing angles, a Multi-orientation simultaneous computation of backprojection for tomographic image reconstruction （MSBP） approach is proposed. In this paper, the filtered backprojection algorithms of CT image reconstruction are realized by using FHT and MSBP. The algorithms may lead to the reduction of the memory space and can reduce the amount of calculation while retaining the precision.