NDLI: Entropic uncertainty inequalities on sparse representation

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Volume 10 (2016) : Issue 3, May

Volume 10 (2016) : Issue 2, Apr

Volume 10 (2016) : Issue 1, Feb

IET Wireless Sensor Systems

Micro & Nano Letters

The Journal of Engineering

Entropic uncertainty inequalities on sparse representation

Content Provider	IET Digital Library
Author	Guanlei, Xu Xiaotong, Wang Xiaogang, Xu
Abstract	In this study, some new entropic inequalities on sparse representation for pairs of bases are investigated. First, the generalised Shannon entropic uncertainty principle and the generalised Rényi entropic uncertainty principle via new derived Hausdorff–Young inequality are proved. These new derived uncertainty principles show that signals cannot have unlimited concentration related to minimum entropies in pairs of bases. Second, the conditions of uniqueness of sparse representation under minimum entropies are given. This study also demonstrates that the entropic greedy-like algorithms can achieve the ‘sparsest’ representation for minimum entropies approximately. Third, the relations between the minimum l 0 solution and minimum entropy are discussed as well. It shows that even if the sparsest representation of l 0-norm is obtained, the entropy cannot always be the minimum and it is possible that the entropy is limited to a interval. These new derived inequalities will be primarily to contribute to a better understanding of sparse representation in the sense of limited entropic uncertainty bounds. Finally, the experiments are shown to verify the authors’ ideas.
Starting Page	413
Ending Page	421
Page Count	9
ISSN	17519675
Volume Number	10
e-ISSN	17519683
Issue Number	Issue 4, Jun (2016)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/10/4
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2014.0072
Journal	IET Signal Processing
Publisher Date	2016-06-01
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Entropic Greedy-like Algorithm Generalised Rényi Entropic Uncertainty Principle Generalised Shannon Entropic Uncertainty Principle Greedy Algorithm Hausdorff-Young Inequality L0-norm Sparse Signal Representation Minimum Entropic Uncertainty Inequality Minimum Entropy Method Signal Processing And Detection Signal Processing Theory Signal Representation
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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