Application of multiplicative regularization for electrical impedance tomography

A multiplicative regularization scheme with edge-preserving characteristics is applied to the inversion of electrical impedance tomography (EIT) data. This scheme employs a multiplicative cost function of a weighted L2-norm regularization function and the data misfit function. It avoids the use of a weighting factor when the regularization term is added to the cost function and allows an adaptive weighting between data misfit and the regularization function. Gauss-Newton method is used to minimize the multiplicative cost function. In this work, we extend the weighted L2-norm regularization scheme onto a triangular grid with an updated formula for gradient and divergence operators. This scheme is tested using synthetic data. The reconstructed images show good piecewise constant characteristics and noise-resistance performance.