超声逆散射成像问题中的截断完全最小二乘法
Application of Truncated Total Least Squares in Ultrasound Inverse Scattering Imaging
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摘要: 在超声逆散射成像问题中 ,由于要反复迭代求物体内部的全场与未知函数 ,使得方程组的系数矩阵与数据项均存在误差 ,将同时考虑系数矩阵和数据项均存在误差的截断完全最小二乘正则化方法运用于超声逆散射成像问题中 数值仿真结果显示 ,截断完全最小二乘法与传统的Tikhonov的正则化方法相比 ,可以提高数据的拟合程度 ,也即提高了成像的质量Abstract: In ultrasound inverse scattering imaging,in order to improve imaging quality,the approximate total field and the unknown function should iteratively be solved. Hence,the coefficient matrices and the data of the linear equation system are both contaminated by error or noise. A truncated total least squares method is proposed,in which the error or noise in both sides of the linear equation system is considered simultaneously to solve the ultrasound inverse scattering imaging problem. Simulation results show that the truncated total least squares method can improve the goodness of fit and the quality of imaging.
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