Abstract:
The problem of numerical piece-uniform regularization of two-dimensional ill-posed problems with bounded
discontinuous solutions are under consideration. The functions of two variables with bounded variations of
several kinds (total variation, variation of Arzela) are applied to solve the problem by use of regularizing
algorithms. In finite-dimensional form, these algorithms are reduced to solution of mathematical programming
mith non-smooth target functions or with non-smooth restrictions. After smooth approximation, the algorithms
are effectively implemented numerically and ensure piece-uniform convergence of approximate solutions to
exact solution to be found. The numerical experiments in problems of distored image reconstruction illustrate
the influence of different kinds of variations on the quality of obtained solution.
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