多小波有限元法在扩散光层析图像重建中的应用研究

Diffuse Optical Tomography Reconstruction Algorithm Based on Multi-Wavelet Finite Element Method

基于有限元法能够快速求解扩散光层析成像的正向过程,即扩散方程(微分方程)的数值解。传统方法一般采用多项式插值作为有限元方程的基函数,易造成其精度不高及效率低的问题,利用多小波函数作为有限元方法中的基函数,可以更快的逼近数值解,且精度更高。实验完成了有限元方法对正向过程的求解和牛顿迭代法对逆向过程的图像重建。通过对于非均匀组织体的实验仿真,分析了基于多小波有限元方法对于正向过程求解的有效性,以及有限元的不同网格划分方式对于重建结果的速度和精度的影响。

The finite element method is used to quickly solve the forward process of diffuse optical tomography, which is the numerical solution of diffusion equation （ differential equations）. Traditional method usually use polynomi- al interpolation as a basis functions of finite element equations, that causes its accuracy is not high and low efficiency. The paper employs multiple wavelet function as the basis function of finite element method （ fern）, it can solve the equation faster, and the precision is higher. The forward process is solved by the finite element method and the Newton iterative method is used to reconstruct the image of reverse process. Through the experimental simulation of heterogeneous tissue, the multiple wavelet finite element method is effective.