A robust electrical conductivity imaging method with total variation and wavelet regularization

Abstract

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.

Keywords: Electrical conductivity; Electrical properties tomography (EPT); Phase-based conductivity imaging; Total variation; Tumor; Wavelet regularization.