A hybrid regularization method combining Tikhonov with total variation for electrical resistance tomography

Abstract

Electrical resistance tomography (ERT) is a promising measurement technique in industrial process imaging. However, image reconstruction in ERT is an ill-posed inverse problem. Regularization methods have been developed to solve the ill-posed inverse problem. Since the penalty term is a form of L2-norm, Tikhonov regularization method guarantees the stability of the solution, but it always makes the image edge oversmoothed. Total variation (TV) regularization method has good ability of preserving image edges. A hybrid regularization method, which combines Tikhonov with TV regularization method, is proposed to get better reconstructed images. The choice of the adaptive weighted parameter between TV and Tikhonov penalty term has been discussed in detail. In the proposed hybrid regularization method, the function of conductivity gradients is used as the adaptive weighted parameter to control automatically the weighting between the penalty terms from TV and Tikhonov regularization. For the model with sharp edges, the proportion of the penalty term from TV regularization is increased to preserve the edges, while for the model with smooth edges, the proportion of penalty term from Tikhonov regularization is increased to make the solution stable and robust to noise. Both simulation and experimental results of Tikhonov, TV and hybrid regularization method are shown respectively, which indicates that the hybrid regularization method can improve the reconstruction quality with sharp edges and is more robust to noise, and it is applicable for models with different edge characteristic.