基于高斯牛顿法的磁纳米温度快速反演算法

Fast inversion algorithm for magnetic nanoparticle temperature based on Gauss-Newton algorithm

根据磁纳米粒子磁化响应强度的奇次谐波信号,构建磁纳米粒子温度测量模型,并将温度模型的反演问题转化为非线性方程组的求解问题.采用一种基于改进型高斯牛顿法的温度快速反演算法,与传统高斯牛顿法进行对比,从温度反演角度研究不同算法对测温精度和时间分辨率的影响.仿真结果表明：该算法具有显著的高稳定性和快收敛性优点,能够达到磁纳米温度计在医学领域应用所需要的测温精度（0.1℃）、时间分辨率（1 s）的要求.

According to the odd harmonic signal of magnetic nanoparticle magnetization response intensity,a temperature measurement model of magnetic nanoparticles was built,and the inversion problem of temperature model was transformed into nonlinear equations solving problem.A fast temperature inversion algorithm based on the improved Gauss-Newton algorithm was proposed,and compared with the traditional Gauss-Newton algorithm.The influence of different algorithms on the accuracy and time resolution of temperature measurement from the temperature inversion view was studied.The simulation results show that the improved Gauss-Newton algorithm has the obvious advantages of high stability and fast convergence,which can meet the requirements of temperature measurement accuracy of 0.1 ℃ and time resolution of 1 s for the application of magnetic nanoparticle thermometers in medical field.