基于自诊断正则化的电阻抗成像逆问题研究

Study on the inverse problem of electrical impedance tomography based on self-diagnosis regularization

电阻抗成像逆问题具有严重的病态性,制约着电阻抗成像的临床应用。正则化是提高电阻抗成像逆问题求解稳定性和图像分辨率的重要数值手段。本文基于吉洪诺夫正则化和对角权重正则化(DWRM),提出了一种自诊断正则化方法。首先基于灵敏度分析电阻抗成像逆问题的病态性,其次运用奇异值理论对自诊断正则化方法进行分析,最后运用几种不同正则化方法进行了电阻抗成像仿真实验和水槽模拟实验。实验结果表明,本文提出的自诊断正则化方法较传统的正则化方法提高了电阻抗成像的图像质量和抗噪声能力,其改进算法有效降低了电阻抗成像的逆问题病态性,有利于推动电阻抗成像的实际运用。

The inverse problem of electrical impedance tomography（EIT） is seriously ill-posed, which restricts the clinical application of EIT. Regularization is an important numerical method to improve the stability of the EIT inverse problem as well as the resolution of the imaging. This paper proposes a self-diagnosis regularization method based on Tikhonov regularization and diagonal weight regularization method（DWRM）. Firstly, the ill-posedness of the inverse problem is analyzed by sensitivity. Then, the performance of the self-diagnosis regularization is analyzed through the singular value theory. Finally, some simulated experiments including simulations and flume experiment are carried out and verify that the self-diagnosis regularization has better image quality and anti-noise ability than those of traditional regularization methods. The self-diagnosis regularization method weakens the ill-posedness of inverse problem of EIT and can prompt the practical application of EIT.