Refined support and entropic uncertainty inequalities

2012/10/29 by Benjamin Ricaud, Ricaud, Benjamin, Bruno Torrésani +1 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Sparse and Compressive Sensing Techniques #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.1210.7711

arxiv created 2012/10/29 · openalex publication_date 2012/10/29 · arxiv updated 2012/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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, ℓ^p-norms inequalities are introduced as byproducts of the entropic inequalities.

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