Refined Support and Entropic Uncertainty Inequalities

Ricaud B.; Torresani B.

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Refined Support and Entropic Uncertainty Inequalities

机译：完善的支持和熵不确定性不等式

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摘要

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, $ell^{p}$ norms inequalities are introduced as byproducts of the entropic inequalities.

机译：提出了熵的广义形式（Hirschman–Beckner）和支撑（Elad–Bruckstein）的不确定性原理。此外，通过引入相干性的概括，可以获得支持不等式的锐化版本。在有限维情况下，在某些条件下，给出了这些不等式的极小值。此外， $ ell ^ {p} $ 规范不等式被引入为熵不等式的副产品。

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来源
《IEEE Transactions on Information Theory》 |2013年第7期|4272-4279|共8页
作者
Ricaud B.; Torresani B.;
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作者单位

Signal Processing Lab. 2, EPFL, Lausanne, Switzerland|c|;

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正文语种 eng
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关键词
$ell^{p}$ norms; Frames; Renyi entropy; Shannon entropy; mutual coherence; support inequalities; uncertainty principles;

机译：$ ell ^ {p} $范数;框架;Renyi熵;Shannon熵;相互相干;支持不等式;不确定性原理;

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Refined Support and Entropic Uncertainty Inequalities

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