Multifrequency electrical impedance tomography with total variation regularization

Multifrequency electrical impedance tomography (MFEIT) reconstructs the distribution of conductivity by exploiting the dependence of tissue conductivity on frequency. MFEIT can be performed on a single instance of data, making it promising for applications such as stroke and cancer imaging, where it is not possible to obtain a 'baseline' measurement of healthy tissue. A nonlinear MFEIT algorithm able to reconstruct the volume fraction distribution of tissue rather than conductivities has been developed previously. For each volume, the fraction of a certain tissue should be either 1 or 0; this implies that the sharp changes of the fractions, representing the boundaries of tissue, contain all the relevant information. However, these boundaries are blurred by traditional regularization methods using [Formula: see text] norm. The total variation (TV) regularization can overcome this problem, but it is difficult to solve due to its non-differentiability. Because the fraction must be between 0 and 1, this imposes a constraint on the MFEIT method based on the fraction model. Therefore, a constrained optimization method capable of dealing with non-differentiable problems is required. Based on the primal and dual interior point method, we propose a new constrained TV regularized method to solve the fraction reconstruction problem. The noise performance of the new MFEIT method is analysed using simulations on a 2D cylindrical mesh. Convergence performance is also analysed through experiments using a cylindrical tank. Finally, simulations on an anatomically realistic head-shaped mesh are demonstrated. The proposed MFEIT method with TV regularization shows higher spatial resolution, particularly at the edges of the perturbation, and stronger noise robustness, and its image noise and shape error are 20% to 30% lower than the traditional fraction method.