改进后Ray-Box Intersection权系数矩阵的SART+TVM重建算法

王珏; 程燕; 蔡玉芳; 王慧倩

doi:10.3788/OPE.20162406.1520

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改进后Ray-Box Intersection权系数矩阵的SART+TVM重建算法

信息科学 | 更新时间：2020-08-13

- 改进后Ray-Box Intersection权系数矩阵的SART+TVM重建算法
- SART + TVM reconstruction algorithm based on improved Ray-Box Intersection weight coefficient matrix
- 光学精密工程 2016年24卷第6期页码：1520-1528
- 作者机构：
  
  1. 重庆大学自动化学院重庆,400030
  2. 重庆大学, 光电技术及系统教育部重点实验室ICT研究中心重庆,400044
- 作者简介：
- 基金信息：
  
  国家重大科学仪器设备开发专项（No.2013YQ030629）();国家自然科学基金（No.61471070）()
- DOI：10.3788/OPE.20162406.1520
  中图分类号： TH703
- 收稿日期：2016-02-01，
  
  修回日期：2016-03-30，
  
  纸质出版日期：2016-06-25
- 稿件说明：
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王珏, 程燕, 蔡玉芳等. 改进后Ray-Box Intersection权系数矩阵的SART+TVM重建算法[J]. 光学精密工程, 2016,24(6): 1520-1528

WANG Jue, CHENG Yan, CAI Yu-fang etc. SART + TVM reconstruction algorithm based on improved Ray-Box Intersection weight coefficient matrix[J]. Editorial Office of Optics and Precision Engineering, 2016,24(6): 1520-1528
王珏, 程燕, 蔡玉芳等. 改进后Ray-Box Intersection权系数矩阵的SART+TVM重建算法[J]. 光学精密工程, 2016,24(6): 1520-1528 DOI： 10.3788/OPE.20162406.1520.

WANG Jue, CHENG Yan, CAI Yu-fang etc. SART + TVM reconstruction algorithm based on improved Ray-Box Intersection weight coefficient matrix[J]. Editorial Office of Optics and Precision Engineering, 2016,24(6): 1520-1528 DOI： 10.3788/OPE.20162406.1520.

摘要

针对均匀采样稀疏型重建问题，研究了Ray-Box Intersection和传统的双线性插值两种权系数矩阵计算方法。对Ray-Box Intersection算法的逻辑漏洞进行了改进，利用直线生成法并结合射线斜率和像素位置关系提出了改进算法。该算法利用代数关系求得射线穿过重建区域的起点和终点，然后取不大于其坐标的最大整数，最后采用直线生成法，依据射线斜率沿X或Y方向得到该条射线在投影区域内经过的所有像素块的左下角坐标集合，对于每个像素块，射线与像素块交点距离即为该像素块对射线的加权值。实验结果表明，相比Ray-Box Intersection权系数矩阵算法，改进后算法速度提高了96%，最大峰值信噪比提高了19%；相比双线性插值算法，改进后算法收敛速度更快，在同样时间代价下最大峰值信噪比提高了5%。改进后的Ray-Box Intersection算法能够获得更好的重建图像质量，细节更清晰。

Abstract

Based on the problem of uniform sampling and sparse reconstruction

a research on calculation method for two weight coefficient matrix

including Ray-box Intersection and traditional bilinear interpolation

was conducted. Improvement on logic flaws of Ray-Box Intersection was made

and the improved algorithm was put forward by combining line generating method with the slope of the ray and pixel location. In this algorithm

the starting point and terminal point of the ray across the reconstruction region can be obtained through algebraic relation

and then the maximum integer no greater than its coordination is used to

in accordance with the ray slope along the X direction and Y direction

work out the lower left coordination collection of all pixel blocks passed through by the ray in the projection area using the line generating method. For each pixel block

the distance of intersection point between the ray and pixel block is their weighted value. It indicates that compared with the weight coefficient matrix algorithm of Ray-Box Intersection

speed of the improved one has increased by 96%

and the peak signal to noise ratio has increased by 19%. In comparison with the bilinear interpolation algorithm

rate of convergence of the improved one is faster

and the peak signal to noise ratio has increased by 5% under the same time period. The improved Ray-Box Intersection algorithm can achieve better reconstructed images and clearer details.

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