生物组织光学层析成像技术的理论研究

A NEW IMAGE RECONSTRUCTION ALGORITHM FOROPTICAL TOMOGRAPHY IN TISSUE

本文发展了一种能实现生物组织光学层析成像的理论。文中建立了光在生物组织中的散射模型，并利用格林函数法分析了问题的数学基本解的形式，得到了问题的初始值的解析表达式。利用偏微分方程特征线传播的方法，可以把问题的边界值（即测量值）传递给每层的初始值。然后结合初始值的解析形式，构造出一个目标函数，即可把逐层重构组织光学特性参数的问题转化为逐层控制参数使目标函数具有极小值的优化问题，从而逐层地重构出生物组织的光学特性参数。利用组织光学特性参数重构的结果，借助于计算机的图象处理技术，就可进一步得到组织内部的光学层析结构图象。本文最后给出了一个计算机数值仿真解。

 new image reconstruction algorithm was presented for the optical tomography in tissue. Considering a planar laser pulse obliquely incident on the surface of tissue, the structure of the fundamental solution was analyzed and the equation of the Green function derived together with the explicit form of the initial conditions. The initial value of the Green function was related to the parameters of medium and the incident angle. When the boundary data were propagated to the initial value at certain layer for each incident angle, an objective function was constructed and the inverse problem of optical tomography reduced into an optimal control problem governing by partial differential equation. By using an iterative algorithm(conjugate gradient method), the scattering coefficients and the absorption coefficients were then reconstructed simultaneously layer by layer. The reflection data were required as the input data in the reconstruction algorithm. A detailed algorithm for the reconstruction was presented as well as numerical example.