基于阻尼Gauss-Newton法的光学断层图像重建

针对生物医学中近红外光进行成像问题,简要描述了基于有限元法（FEM）的光学图像重建的过程,提出了光学重建逆问题的阻尼Gauss-Newton算法.该方法定义一个测量与预测数据间误差的目标函数,利用最小二乘问题的结构特点由目标函数一阶导数直接获得Hessian阵以确定下降方向,并在迭代求解中引入线性搜索以确定搜索步长,从而达到快速收敛.数值模拟结果证明该方法在实际应用中的优越性和可行性.

The reconstruction of the optical tomography based on the damped Gauss-Newton algorithm

The image reconstruction process based on the finite element method （FEM）for the near infrared optical imaging in biomedical applications is described firstly and then a damped Gauss-Newton algorithm is proposed for the reconstruction purpose. In this method, the objective function is defined as the difference between the measured and the predicted data. By taking the advantage of the structure of the least-square problem, the Hessian matrix is obtained directly from the first order derivative of the objective function, from which the decreasing direction can be acquired. In order to determine the step for a given decreasing direction and achieve a fast convergence of the reconstruction, the linear search is introduced in the iteration process. Numerical simulation results show the reliability and superiority of this method in actual applications.