为解决三维电阻抗成像(electrical impedance tomography，EIT)逆问题的病态性和改善重建图像质量，在对比研究Tikhonov正则化和一步牛顿法(Newton’s one-step error reconstructor，NOSER)的基础上，提出基于这2种算法的混合正则化算法。采用归一化均方距离判据和归一化平均绝对距离判据，为判断重构图像和原始图像的差异提供一种量化的客观标准。仿真计算和物理模型实验结果表明：混合正则化算法与Tikhonov正则化、NOSER正则化相比，不仅降低了雅克比矩阵的条件数，使逆问题由病态转为良态，还提高了目标物体的空间分辨率，有效改善了图像质量。该混合正则化算法对三维EIT的图像重构是有效的、可靠的。

By studying the reconstructed algorithms of Tikhonov regularization and the Newtons one-step error reconstructor (NOSER),a combined regularization algorithm is proposed. Two evaluation parameters of reconstructed algorithms,i.e. normalization mean square distance criterion(NMSD)and normalized mean absolute distance criterion(NMAD)are used to evaluate the results precision of inverse problem quantificationally. The comparison among Tikhonov regularization,NOSER and the combined regularization shows that the ill-condition and error of inverse problem are reduced. This new algorithm can decrease the condition number by 97%,NMSD by 51% and NMAD by 41% at least. Simulate results show that the combined regularization algorithm can reconstruct the target image in the depth from 10 mm to 40 mm. The performance of this system and the combined regularization algorithm demonstrate significantly better spatial resolution and less reconstructed error.

国家自然科学基金资助项目（50877082，51107150）；中央高校基础科研业务经费（CDJZR10150021）