On uniform approximation on subsets
In the present paper, the author studies a problem in approximation theory that formalizes the problem of approximation of a document photograph's background considered in the theory of image processing. The question under consideration is related to the problem of compressed measurement. It is well known that \(l_1\)-minimization and greedy algorithms (cf. [\textit{D. L. Donoho}, IEEE Trans. Inf. Theory 52, No. 4, 1289--1306 (2006; Zbl 1288.94016); \textit{E. D. Livshits}, Sb. Math. 203, No. 2, 183--195 (2012; Zbl 1259.94019); translation from Mat. Sb. 203, No. 2, 33--44 (2012)]) are among the most effective methods of solving the problem of compressed measurements. In order to solve the problem considered here, the author employs some analogues of the methods mentioned above.
scientific article; zbMATH DE number 6568794