Discretization of a new method for localizing discontinuity lines of a noisy two-variable function

We consider the ill-posed problem of localizing (finding the position of) lines of discontinuity of a noisy function of two variables. New regularizing methods of localization are constructed in a discrete form. In these methods, the averaging kernel is varying, which simplifies the implementation of the algorithms. We obtain estimates for the localization error of the methods and for their separability threshold, which is another important characteristic.