Refined support and entropic uncertainty inequalities

Benjamin Ricaud (1) , Bruno Torrésani (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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 has been obtained by introducing a generalization of the coherence. In the finite dimensional case and under certain conditions, minimizers of this inequalities are given as constant functions on their support. In addition, p -norms inequalities are introduced as byproducts of the entropic inequalities.

Mots clés: mutual coherence

Mots clés: Uncertainty principles; support inequalities; Shannon entropy; Renyi entropy; lp norms; frames; mutual coherence.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Benjamin Ricaud, Bruno Torrésani. Refined support and entropic uncertainty inequalities. IEEE Transactions on Information Theory, 2013, 59 (7), pp.4272-4279. ⟨10.1109/TIT.2013.2249655⟩. ⟨hal-00746976⟩