一种基于共轭梯度最优化技术的三维时域扩散光学层析方法  

Conjugate-Gradient-Based Optimization for Three-Dimensional Time-Domain Diffuse Optical Tomography

作　　者：杨芳[1] 阮平巧[1] 高峰[1] 赵会娟[1] 

机构地区：[1]天津大学精密仪器与光电子工程学院,天津300072

出　　处：《中国激光》2009年第10期2517-2523,共7页Chinese Journal of Lasers

基　　金：国家自然科学基金(30870657;30678049);国家973计划(2006CB705700);国家863计划(2009AA02Z413);天津市自然科学基金(07JCYBJC06600);高等学校创新引智计划(B07014)资助项目

摘　　要：扩散光学层析(DOT)中的图像重建是一个面向大参数集的非线性最优化问题,其标准求解方法为牛顿类迭代法,需要对整个Jacobian矩阵进行构建、求逆和存贮,这对大规模的三维问题是不可行的,为此常采用基于逐行线性逆策略的非创伤性填充(ART)技术,图像质量受到严重制约。采用共轭梯度算法,直接求解非线性目标函数梯度,可避免对Jacobian矩阵的操作,为有效降低步长因子求解引起的附加计算量,采用一维不精确搜索算法。通过对双非均匀目标体的平板模型进行模拟成像,与代数重建算法结果进行比较,表明共轭梯度法的重建质量、收敛速度和收敛性都优于ART算法。The image reconstruction in diffuse optical tomography （DOT） is regarded as a large-scale nonlinear optimization problem,whose solution strategy is usually based on a Newton-like iteration algorithm involving the construction and inversion of the Jacobian matrix. It becomes intractable,when the scale of the inverse problem is large. To overcome this problem,algebraic reconstruction techniques （ART）,an iterative solving method based on row action,is proposed to reduce the computational effort,but which will result in poor image quality. In this paper,conjugate gradient （CG） method is employed here,which requires only the computation of the objective function gradient to avoid calculating and storing the whole Jacobian matrix. Step length is determined by inexact line search method. The proposed methodology is validated by reconstructing the image of the slab phantom containing two deeply-located absorption and scattering contrasting cubes. Compared with ART,we find that the CG method performs better than ART at the image quality ,convergence and the speed of it.

关 键 词：图像处理 时域扩散光学层析 逆问题 共轭梯度算法 不精确线性搜索 

分 类 号：Q63[生物学—生物物理学]