超声逆散射成像问题中的正则化方法研究

Regularization method study in ultrasound inverse scattering imaging

为提高成像质量,需反复地求解不适定逆散射方程,而不适定方程的求解需要正则化处理.将截断完全最小二乘正则化方法应用到迭代过程中,该方法同时考虑逆散射方程的系数矩阵和数据项均存在误差的情况,不仅适合于不适定性较弱的情况,而且适合于不适定性较强的情况,提高了算法的收敛性以及成像的质量.对不同结构以及不同对比度图像的数值仿真结果显示,截断完全最小二乘正则化方法,较只考虑数据项存在误差的Tikhonov正则化方法成像质量高,且适用范围广.

In order to obtain good image quality, the forward and inverse scattering equations must be iteratively solved. The convergence property of these iterative methods depends strongly on the regularization method for dealing with the ill-posed inverse scattering equation. Analysis of the present iterative methods revealed that both the coefficient matrices and the data of linear systems were contaminated by error or noise, while the Tikhonov regularization method only considered the error or noise in data. Truncated total least squares (TTLS) method was proposed for solving the ill-posed inverse scattering equation in the iterative procedure. This method considered the error or noise on both sides of the ill-posed inverse scattering equation simultaneously, so it was not only suited for weak ill-posed problem, but also suited for strong ill-posed problem. Simulation results for the images with different structure and contrast show that TTLS method can yield high quality image and its application field is larger than that of Tikhonov regularization method.