Title :
Refined Support and Entropic Uncertainty Inequalities
Author :
Ricaud, B. ; Torresani, Bruno
Author_Institution :
Signal Process. Lab. 2, EPFL, Lausanne, Switzerland
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;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2013.2249655
