Lagrange interpolation reprojection-revising reconstruction with incomplete data in optical computed tomography
Lagrange interpolation reprojection-revising reconstruction with incomplete data in optical computed tomography
复制标题
光学计算机断层扫描中不完整数据的拉格朗日插值重投影修正重建
DOI：
10.1117/1.3475948
复制
发表时间：
2010-08-01
影响因子：
1.3
通讯作者：
Liu, Lei
中科院分区：
文献类型：
--
作者：
Wan, Xiong;Yi, Jianglin;Liu, Lei
在针对包括障碍物的场的光学计算机断层扫描（OpCT）重建的情况下，投影数据的部分丢失;因此，如果不采用其他预处理或插值方法，则使用常规OpCT算法的图像重建将总是不精确的。针对不完整数据的重建问题，提出了一种拉格朗日插值重投影修正（LIRR）算法。首先采用拉格朗日插值多项式对丢失的投影数据进行预估。在迭代过程中，通过与粗重建图像的重投影比较，保留无偏的拉格朗日插值估计，否则，利用插值数据和重投影数据的加权叠加逐射线修正有偏估计。重复这些步骤，直到丢失数据的所有估计都是可接受的。比较了几种已知算法和LIRR算法对两种典型实验图像（包括圆形不透明物体）的重建结果。此外，还设计了发射光谱层析成像实验来评估LIRR。仿真和实验结果表明，LIRR算法在重建精度上比传统的OpCT算法有了很大的提高，在不完全数据的OpCT重建中具有潜在的应用价值。
In the case of optical computed tomography (OpCT) reconstructions for the field comprising obstacle objects, parts of the projection data are lost; hence, the image reconstruction would be always imprecise with conventional OpCT algorithms if no other preprocessing or interpolation approaches are adopted. To solve the problem of the reconstruction with incomplete data, a Lagrange interpolation reprojection-revising (LIRR) algorithm is proposed. First a Lagrange interpolation polynomial is adopted to preestimate the lost projection data. By comparing to the reprojection of the rough reconstructed image in the iteration, the unbiased Lagrange interpolation estimations are retained; otherwise, the biased estimations are revised, ray by ray, with the weighed superposition of the interpolation and the reprojection data. These steps are repeated until all estimations for lost data are acceptable. Reconstruction results of some known algorithms and the LIRR algorithm for two typical tested images, including a circle round opaque object, were compared. Additionally, an emission spectral tomography experiment was also designed to evaluate the LIRR. The simulation and experiment results show the LIRR makes a great improvement in reconstruction precision over the traditional OpCT algorithms and hence has potential application of OpCT reconstructions with incomplete data.