Numerical piecewise-uniform regularization for two-dimensional ill-posed problems

The problem of piecewise-uniform regularization for two-dimensional ill-pos ed problems with bounded discontinuous solutions is under discussion. The a lgorithm of modified Tikhonov regularization is applied to solve the proble m on the class of functions of two variables with bounded VH-variation as p reviously proposed by the author. In finite-dimensional form, the algorithm is reduced to mathematical programming with a nonsmooth target function. A fter smooth approximation, the algorithm is numerically implemented in an e ffective way to ensure the piecewise-uniform convergence of the approximate solutions to the exact solution of an ill-posed problem. The quality of ob tained piecewise-uniform regularization is illustrated by numerical experim ents in blurred and noisy image reconstruction.