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A method of spatially adaptive Lp regularization for electrical tomography

Electrical tomography (ET) is a promising technology to visualize the distribution of electrical properties. The image reconstruction of ET is an ill-posed nonlinear inverse problem. So the regularization methods are introduced to treat the ill-posedness. Considering the fact that L2 regularization always makes the solution too smooth and L1 regularization always makes the solution too sparse, Lp regularization method emerged. A proper parameter p can make the regularized solution more close to the real solution. So a spatially adaptive p selection method is proposed for regularizing the inverse problem of ET based on Lp regularization. The proposed method adaptively updates the parameter p during the iteration process and provides spatially varying parameter p for each pixel of the reconstructed image. The method is discussed using simulated data for some typical conductivity distributions, and further verified with the practical ERT system. Both simulation and experimental results demonstrate that the spatially adaptive method obtains different p distributions for different object distributions. This method achieves an efficient and reliable regularization solution and improves the quality of the reconstructed image.