Image enhancement by total variation quasi-solution method

A new method of image restoration based on the quasi-solution method for a compact set of functions with bounded total variation is introduced. Application of this method does not require estimation of the noise level, which is necessary to choose the regularization parameter in the Tikhonov regularization method. The approbation of this method with test images shows its effectiveness for image deringing. The text was submitted by the authors in English. Andrey S. Krylov. Born 1956. Graduated from the Faculty of Computational Mathematics and Cybernetics, Moscow State University (MGU). Received the degree of PhD in 1983. Currently an associate professor and head of the Laboratory of Mathematical Methods of Image Processing at the Faculty of Computational Mathematics and Cybernetics, MGU. His main research interests lie in mathematical methods of multimedia data processing. Vladimir N. Tsibanov. Born 1982. Graduated from the Faculty of Computational Mathematics and Cybernetics, Moscow State University (MGU). He is currently a PhD student at the Faculty of Computational Mathematics and Cybernetics, MGU. His main research interests lie in variational methods in image processing. Alexander M. Denisov. Born 1946. Graduated from the Faculty of Mechanics and Mathematics, Moscow State University (MGU). Received the degrees of PhD in 1972 and doctor of science in 1987. Currently a professor and head of the Chair of Mathematical Physics of the Faculty of Computational Mathematics and Cybernetics, MGU. His main research interests lie in inverse and ill-posed problems in mathematical physics.