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Abstract. 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 2 l norm regularisation. However, the non-differentiability of TV regularisation has led to the use of different algorithms. Recent advances in TV algorithms such as Primal Dual Interior Point Method (PDIPM), Linearised Alternating Direction Method of Multipliers (LADMM) and Spilt Bregman (SB) method have all been demonstrated successfully for 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; SB had a faster convergence rate than PDIPM and the lowest image error.

A new reconstruction algorithm for electrical capacitance tomography (ECT) is proposed. The basic idea behind this algorithm is to model the forward problem by using multiple linear regression, then obtain a stabilized solution of the inverse problem by using a regularization technique. This algorithm is numerically simple and computationally fast because it involves only a single matrix-vector multiplication when reconstructing an image. Tests performed on experimental and simulation data indicate that this algorithm can provide images superior to those obtained with the linear back-projection (LBP) algorithm, with a similar reconstruction time.

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