On uniform approximation on subsets
type: Item
instance of: scholarly article
title: On uniform approximation on subsets
zbMATH Open document ID: 1337.94005
DOI: 10.1134/S0001434615110176
author: E. D. Livshits
published in: Mathematical Notes
publication date: 2016-04-14T00:00:00Z
review text: 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.
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 6568794
zbMATH Keywords: image processing
zbMATH Keywords: uniform approximation on subsets
zbMATH Keywords: background approximation problem
zbMATH Keywords: greedy algorithm
zbMATH Keywords: compressed measurement
zbMATH Keywords: Nikol'skiĭ's inequality
MaRDI profile type: Publication
cites work: Compressed sensing
cites work: Q3961321
description: scientific article; zbMATH DE number 6568794