New selection methods of regularization parameter for electrical resistance tomography image reconstruction

摘要

Image reconstruction in Electrical Resistance Tomography (ERT) is a nonlinear and ill-posed inverse problem. The standard Tikhonov regularization method is always used to solve the ERT problem. However, in Tikhonov method, to guarantee the optimization problem have a solution, usually the regularization parameter matrix always is composed of diagonal matrix, and all the diagonal elements in the matrix are equal to each other. Under this condition, much useful information must be lost. In this paper, two new selection methods of regularization parameter are proposed, which could make the most of sensitivity coefficient matrix. The new methods use l1 norm and l2 norm of sensitivity coefficient matrix respectively to reconstitute regularization parameter. Experiments result proved the two methods could obtain better space resolution than the standard Tikhonov regularization optimization method.