电阻抗成像正则化参数的优化方法

为改善电阻抗成像逆问题的不适定性，通常采用Tikhonov正则化算法来求得适当的解。正则化参数对重建图像的质量和计算速度影响较大。笔者提出了一种基于残差范数和解范数乘积的优化方法(PRS)求取电阻抗成像的正则化参数。为验证该方法的有效性，笔者针对不同的目标大小、目标位置、目标电导率、目标数目以及不同程度的噪声分别进行了重建图像的仿真实验和水槽实验。结果表明：这种优化方法可以快速找到相对最优的正则化参数，且具有良好的抗噪性能。与传统的L曲线方法相比，提高了图像重建质量。

Optimization of regularization parameters for electricalimpedance tomography

The image quality and computation speed are bounded up with regularization parameters. To improve the ill-posed property of the inverse problem of electrical impedance tomography (EIT), a novel approach, which is based on the product of the residual norm and the solution norm(PRS), is presented to optimize the Tikhonov regularization parameters of EIT. To verify the feasibility and effectiveness of the proposed method, five simulations of image reconstruction, together with a tank experiment, have been carried out with considering different sizes, locations, conductivity distributions and numbers of the target areas as well as the scenarios of the data with noises. The encouraging results demonstrate that the proposed optimization approach can identify the relatively optimal regularization parameter quickly and has better noise immunity, and it also enhances the quality of the reconstructed images significantly compared with the conventional L-curve method.