A discrete algorithm for the localization of lines of discontinuity of a two-variable function

We consider an ill-posed problem for the localization of lines of discontinuity. It is assumed that, instead of the exact function $f$, we know the values at the points of the uniform grid of the mean squares of the disturbed function $f^\delta$, $\|f-f^\delta\|_{L_2(\mathbb R^2)}\le\delta$, and the level of the error $\delta$. We construct an algorithm for the localization of lines of discontinuity, prove its convergence with approximation accuracy estimates whose order coincides with that of the estimates obtained earlier by the authors for the case when the function itself is given instead of the mean values of $f^\delta$. We also justify estimates for an important characteristic of the algorithm, separability threshold.