A modified L-curve method for choosing regularization parameter in electrical resistance tomography

Abstract

Regularization methods are widely used in dealing with the ill-posed inverse problem of electrical resistance tomography (ERT), especially the Tikhonov method. A proper choice of regularization parameter is crucial to produce an efficient regularization solution. As a regularization parameter choice method, L-curve method is popular for its simpleness and intuition. However there is no guarantee that the method can always determine a proper parameter for all situations of ERT. The investigation on those failed situations shows that a new corner point often appears on the curve and the parameter corresponding to the new corner point can obtain a better solution than the one corresponding to the traditional global corner point. Therefore a modified L-curve method is proposed based on the new corner point. Moreover two strategies are provided to implement the modified method: one computes the new corner point by means of the second-order differential of L-curve, and another computes the new corner point with the help of the curvature of L-curve. The modified L-curve method is verified by numerical simulations of some typical distributions in ERT. And the results indicate that the modified method can achieve an efficient solution and implement the image reconstruction where the traditional L-curve method cannot. The modified L-curve method extends the application of L-curve in the field of choosing regularization parameter and can also be applied in other kinds of tomography.