• DocumentCode
    73611
  • Title

    Refined Support and Entropic Uncertainty Inequalities

  • Author

    Ricaud, B. ; Torresani, Bruno

  • Author_Institution
    Signal Process. Lab. 2, EPFL, Lausanne, Switzerland
  • Volume
    59
  • Issue
    7
  • fYear
    2013
  • fDate
    Jul-13
  • Firstpage
    4272
  • Lastpage
    4279
  • Abstract
    Generalized versions of the entropic (Hirschman- Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality is obtained by introducing a generalization of the coherence. In the finite-dimensional case and under certain conditions, minimizers of these inequalities are given. In addition, lp norms inequalities are introduced as byproducts of the entropic inequalities.
  • Keywords
    entropy; ήnite-dimensional case; Elad-Bruckstein uncertainty principle; Hirschman-Beckner uncertainty principle; entropic uncertainty inequalities; lp norms inequalities; refined support; Coherence; Context; Entropy; Fourier transforms; Hilbert space; Uncertainty; Vectors; $ell^{p}$ norms; Frames; Renyi entropy; Shannon entropy; mutual coherence; support inequalities; uncertainty principles;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2013.2249655
  • Filename
    6471825
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=73611