Localization of boundaries for subsets of discontinuity points of noisy function

We consider ill-posed problem of localization of discontinuities of the first kind of function in one variable under condition that in metric $L_2$ there are given approximately measured function and a level of inaccuracy. We propose a new statement of the problem when all discontinuities can be divided into subsets and localization is performed for subsets of discontinuities. Under additional assumption that all discontinuities possess jumps of one sign we construct new regular method which admits to determine a number of subsets of discontinuities and to approximate their boundaries with estimation of approximation accuracy.