Chang J, Graber H L, Barbour R L
J Biomed Opt. 1998 Apr;3(2):137-44. doi: 10.1117/1.429870.
By applying linear perturbation theory to the radiation transport equation, the inverse problem of optical diffusion tomography can be reduced to a set of linear equations, Wμ=R, where W is the weight function, μ are the cross-section perturbations to be imaged, and R is the detector readings perturbations. We have studied the dependence of image quality on added systematic error and/or random noise in W and R. Tomographic data were collected from cylindrical phantoms, with and without added inclusions, using Monte Carlo methods. Image reconstruction was accomplished using a constrained conjugate gradient descent method. Results show that accurate images containing few artifacts are obtained when W is derived from a reference state whose optical thickness matches that of the unknown test medium. Comparable image quality was also obtained for unmatched W, but the location of the target becomes more inaccurate as the mismatch increases. Results of the noise study show that image quality is much more sensitive to noise in W than in R, and the impact of noise increases with the number of iterations. Images reconstructed after pure noise was substituted for R consistently contain large peaks clustered about the cylinder axis, which was an initially unexpected structure. In other words, random input produces a nonrandom output. This finding suggests that algorithms sensitive to the evolution of this feature could be developed to suppress noise effects. © 1998 Society of Photo-Optical Instrumentation Engineers.
通过将线性微扰理论应用于辐射传输方程，光学扩散断层成像的逆问题可以简化为一组线性方程(W\mu = R)，其中(W)是权重函数，(\mu)是待成像的截面微扰，(R)是探测器读数微扰。我们研究了图像质量对(W)和(R)中添加的系统误差和/或随机噪声的依赖性。使用蒙特卡罗方法从有或没有添加内含物的圆柱形体模中收集断层数据。使用约束共轭梯度下降法完成图像重建。结果表明，当(W)从光学厚度与未知测试介质相匹配的参考状态导出时，可以获得包含少量伪影的准确图像。对于不匹配的(W)也获得了可比的图像质量，但随着不匹配程度的增加，目标的位置变得更加不准确。噪声研究结果表明，图像质量对(W)中的噪声比对(R)中的噪声更敏感，并且噪声的影响随着迭代次数的增加而增加。用纯噪声代替(R)后重建的图像始终包含围绕圆柱轴聚集的大峰值，这是一个最初意想不到的结构。换句话说，随机输入产生非随机输出。这一发现表明，可以开发对该特征演变敏感的算法来抑制噪声影响。© 1998 光电仪器工程师协会。
