Method of Tikhonov Regularization for Weighted Frequency-Difference Electrical Impedance Tomography

Frequency-difference electrical impedance tomography (fdEIT) has attracted considerable attention, which can visualize anomalies without requiring any time-reference data obtained in the absence of anomalies and alleviate undesirable effects of modeling errors. Simple frequency-difference (SFD) method and weighted frequency-difference (WFD) method are two existing algorithms. Besides, WFD perform better due to its high resolution in the condition where the conductivity of background changes much. However, truncated singular value decomposition (TSVD) regularization adopted in WFD have several problems such as difficulties to choose the accurate truncation parameter, unsatisfactory image quality even in low noise condition and overwhelming computational tasks for large-scale problems. In this paper, an improved WFD algorithm using Tikhonov regularization (WFDTR) method as well as the selection method of regularization parameter is proposed. This method can figure out the appropriate regularization parameter more easily through L curve method and acquire reconstructed distribution images of good quality. What's more, the second corner of L curve is investigated. Finally, the proposed method has been compared with the conventional WFD method through numerical simulations. The proposed method works better than WFD in relatively low noise cases according to localization error, shape error as well as image noise indexes. In relatively high noise condition, they perform approximately equally.