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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 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. [ABSTRACT FROM AUTHOR]

The applications of total variation (TV) algorithms for electrical impedance tomography (EIT) have been investigated. The use of the TV regularisation technique helps to preserve discontinuities in reconstruction, such as the boundaries of perturbations and sharp changes in conductivity, which are unintentionally smoothed by traditional norm regularisation. However, the non-differentiability of TV regularisation has led to the use of different algorithms. Recent advances in TV algorithms such as the primal dual interior point method (PDIPM), the linearised alternating direction method of multipliers (LADMM) and the spilt Bregman (SB) method have all been demonstrated successful EIT applications, but no direct comparison of the techniques has been made. Their noise performance, spatial resolution and convergence rate applied to time difference EIT were studied in simulations on 2D cylindrical meshes with different noise levels, 2D cylindrical tank and 3D anatomically head-shaped phantoms containing vegetable material with complex conductivity. LADMM had the fastest calculation speed but worst resolution due to the exclusion of the second-derivative; PDIPM reconstructed the sharpest change in conductivity but with lower contrast than SB; SB had a faster convergence rate than PDIPM and the lowest image errors. [ABSTRACT FROM AUTHOR]