Geodesic
Application of function of several variables with bounded variation to numerical solution of two-dimensional ill-posed problems
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 3, pp. 257-271

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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. 
@article{SJVM_1999_2_3_a4,
     author = {A. S. Leonov},
     title = {Application of function of several variables with bounded variation to numerical solution of two-dimensional ill-posed problems},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {257--271},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_3_a4/}
}
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A. S. Leonov. Application of function of several variables with bounded variation to numerical solution of two-dimensional ill-posed problems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 3, pp. 257-271. http://geodesic.mathdoc.fr/item/SJVM_1999_2_3_a4/