Abstract
The problem of piecewise-uniform regularization for two-dimensional ill-posed problems with bounded discontinuous solutions is under discussion. The algorithm of modified Tikhonov regularization is applied to solve the problem on the class of functions of two variables with bounded VH-variation as previously proposed by the author. In finite-dimensional form, the algorithm is reduced to mathematical programming with a nonsmooth target function. After smooth approximation, the algorithm is numerically implemented in an effective way to ensure the piecewise-uniform convergence of the approximate solutions to the exact solution of an ill-posed problem. The quality of obtained piecewise-uniform regularization is illustrated by numerical experiments in blurred and noisy image reconstruction.
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