Publication Details

Řídké reprezentace signálů: úvod do problematiky

ŠPIŘÍK Jan, HRBÁČEK Radek, RAJMIC Pavel and VESELÝ Vítězslav. Řídké reprezentace signálů: úvod do problematiky. Elektrorevue - www.elektrorevue.cz, vol. 2011, no. 50, pp. 1-10. ISSN 1213-1539. Available from: http://elektrorevue.cz/cz/download/ridke-reprezentace-signalu--uvod-do-problematiky/
English title
Introduction to sparse signal representations
Type
journal article
Language
czech
Authors
Špiřík Jan, Ing. (FEEC BUT)
Hrbáček Radek, Ing. (DCSY FIT BUT)
Rajmic Pavel, doc. Mgr., Ph.D. (UTKO FEEC BUT)
Veselý Vítězslav, doc. RNDr., CSc. (DM OSO FME BUT)
URL
Keywords

signal proccesing, sparse, systems of linear equations, l1-relaxation, NSP, RIP, greedy algorithms, compressed sensing

Abstract

The article is an introduction to the sparse signal representation, that could be understood as an underdetermined system of linear equations, where exists a solution having only a very few non-zero coefficients. The article presents the theoretical solutions on examples and pictures and does not deal with excessive details. The paper is also focused on conditions of uniqueness of the solution, solving the problem via l1-optimization and usefull restricted isometry property (RIP). Some algorithms for finding sparse solutions are also presented. Another article immediately follows and is called "Sparse signal representations: Compressed sensing", which introduces one of the most attractive applications.

Published
2011
Pages
1-10
Journal
Elektrorevue - www.elektrorevue.cz, vol. 2011, no. 50, ISSN 1213-1539
Book
Elektrorevue - Internetový časopis (http://www.elektrorevue.cz)
Place
Brno, CZ
BibTeX 
@ARTICLE{FITPUB10427,
   author = "Jan \v{S}pi\v{r}\'{i}k and Radek Hrb\'{a}\v{c}ek and Pavel Rajmic and V\'{i}t\v{e}zslav Vesel\'{y}",
   title = "\v{R}\'{i}dk\'{e} reprezentace sign\'{a}l\r{u}: \'{u}vod do problematiky",
   pages = "1--10",
   booktitle = "Elektrorevue - Internetov\'{y} \v{c}asopis (http://www.elektrorevue.cz)",
   journal = "Elektrorevue - www.elektrorevue.cz",
   volume = 2011,
   number = 50,
   year = 2011,
   location = "Brno, CZ",
   ISSN = "1213-1539",
   language = "czech",
   url = "https://www.fit.vut.cz/research/publication/10427"
}
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