Purpose

This study aims to develop and evaluate a robust conductivity imaging method that combines total variation and wavelet regularization to enhance the accuracy of conductivity maps.

Theory and methods

The proposed approach is based on a gradient-based method. The central equation is derived from Maxwell's equation and describes the relationship between conductivity and the transceive phase. A linear system equation is obtained via a finite-difference method and solved using a least-squares method. Total variation and wavelet transform regularization terms are added to the minimization problem and solved using the Split Bregman method to improve reconstruction stability. The proposed approach is compared with conventional and gradient-based methods. Numerical simulations are performed to validate the accuracy of the developed method, and the effects of noise are determined. Phantom and in vivo experiments are conducted at 3 T to verify the clinical applicability of the proposed method.

Results

Numerical simulations show that the proposed method is more robust than other methods and can suppress the effects of noise. The quantitative conductivity value of the phantom experiment agrees with the measured value. The in vivo experiment results present a clear structure, and the conductivity value of the tumor region is significantly higher than that around healthy tissues.

Conclusion

The proposed electrical conductivity imaging method can improve the quality of conductivity reconstruction, and thus, has future clinical applications.

中文翻译：

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具有总变化和小波正则化的鲁棒电导率成像方法。

目的

这项研究旨在开发和评估一种可靠的电导率成像方法，该方法将总变化量和小波正则化相结合以提高电导率图的准确性。

理论与方法

所提出的方法基于基于梯度的方法。中心方程式是从麦克斯韦方程式导出的，描述了电导率和收发相位之间的关系。线性系统方程是通过有限差分法获得的，并使用最小二乘法求解。将总变异和小波变换正则项添加到最小化问题中，并使用Split Bregman方法求解，以提高重建稳定性。将该方法与常规方法和基于梯度的方法进行了比较。进行数值模拟以验证所开发方法的准确性，并确定噪声的影响。在3 T下进行幻像和体内实验，以验证所提出方法的临床适用性。

结果

数值仿真表明，该方法比其他方法具有更强的鲁棒性，并且可以抑制噪声的影响。体模实验的定量电导率值与测量值一致。体内实验结果显示结构清晰，肿瘤区域的电导率值明显高于健康组织周围。

结论

提出的电导率成像方法可以提高电导率重建的质量，因此具有未来的临床应用。