CAJ | 학술논문

在求解扩散光学断层成像中的正向问题时,目前普遍采用有限元法,但是随着实际模型规模的增大,有限元法的计算量问题日益显著,而边界元法则由于可以降低计算维度使计算量减少而备受关注.本文以均匀的高散射介质为模型,研究了将快速多极边界元法用于扩散光学断层成像的正向问题.快速多极边界元法利用核函数的多极展开,将常规边界元法中系数矩阵和迭代矢量的乘积项等价为相应四叉树结构的一次递归,再结合广义最小残量法进行迭代求解.将计算结果和蒙特卡罗法的模拟结果进行了比较,表明利用快速多极边界元法的模拟结果和蒙特卡罗法的结果有很好的一致性.研究结果验证了快速多极边界元法可以用于扩散光学断层成像,为其大规模和实时成像带来可观的前景.
재구해확산광학단층성상중적정향문제시,목전보편채용유한원법,단시수착실제모형규모적증대,유한원법적계산량문제일익현저,이변계원법칙유우가이강저계산유도사계산량감소이비수관주.본문이균균적고산사개질위모형,연구료장쾌속다겁변계원법용우확산광학단층성상적정향문제.쾌속다겁변계원법이용핵함수적다겁전개,장상규변계원법중계수구진화질대시량적승적항등개위상응사차수결구적일차체귀,재결합엄의최소잔량법진행질대구해.장계산결과화몽특잡라법적모의결과진행료비교,표명이용쾌속다겁변계원법적모의결과화몽특잡라법적결과유흔호적일치성.연구결과험증료쾌속다겁변계원법가이용우확산광학단층성상,위기대규모화실시성상대래가관적전경.
@@@@The forward problem of diffuse optical tomography (DOT) is commonly solved by the finite element method (FEM) currently. However, with the increase of the model scale, the computational complexity of FEM increases significantly; while the boundary element method (BEM) attracts much attention because of its reduction in calculated dimensions. In this paper, the fast multipole boundary element method (FMBEM) for DOT is studied using a model of highly scattering homogenous medium. In FMBEM, by the multipole expansions of kernel functions, the product of matrix coefficient and iterative vector can be equivalent to the recursion of a quadtree;and then a generalized minimal residual method is used to solve the BEM equation iteratively. The calculations of the FMBEM are compared with Monte Carlo simulations. The results show that the calculations of the FMBEM are in good agreement with Monte Carlo simulations. This demonstrates the feasibility of FMBEM in DOT and indicates that the FMBEM has a bright future for large-scale and real-time imaging.