Best bases for signal spaces

Yonathan Aflalo; Haïm Brezis; Alfred Bruckstein; Ron Kimmel; Nir Sochen

doi:10.1016/j.crma.2016.10.002

Best bases for signal spaces

Translated title of the contribution: Best bases for signal spaces

Yonathan Aflalo, Haïm Brezis, Alfred Bruckstein, Ron Kimmel, Nir Sochen

Technion - Israel Institute of Technology, Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We discuss the topic of selecting optimal orthonormal bases for representing classes of signals defined either through statistics or via some deterministic characterizations, or combinations of the two. In all cases, the best bases result from spectral analysis of a Hermitian matrix that summarizes the prior information we have on the signals we want to represent, achieving optimal progressive approximations. We also provide uniqueness proofs for the discrete cases.

Translated title of the contribution	Best bases for signal spaces
Original language	English
Pages (from-to)	1155-1167
Number of pages	13
Journal	Comptes Rendus Mathematique
Volume	354
Issue number	12
DOIs	https://doi.org/10.1016/j.crma.2016.10.002
State	Published - 1 Dec 2016

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2016.10.002

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title = "Best bases for signal spaces",

abstract = "We discuss the topic of selecting optimal orthonormal bases for representing classes of signals defined either through statistics or via some deterministic characterizations, or combinations of the two. In all cases, the best bases result from spectral analysis of a Hermitian matrix that summarizes the prior information we have on the signals we want to represent, achieving optimal progressive approximations. We also provide uniqueness proofs for the discrete cases.",

author = "Yonathan Aflalo and Ha{\"i}m Brezis and Alfred Bruckstein and Ron Kimmel and Nir Sochen",

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T1 - Best bases for signal spaces

AU - Aflalo, Yonathan

AU - Brezis, Haïm

AU - Bruckstein, Alfred

AU - Kimmel, Ron

AU - Sochen, Nir

PY - 2016/12/1

Y1 - 2016/12/1

N2 - We discuss the topic of selecting optimal orthonormal bases for representing classes of signals defined either through statistics or via some deterministic characterizations, or combinations of the two. In all cases, the best bases result from spectral analysis of a Hermitian matrix that summarizes the prior information we have on the signals we want to represent, achieving optimal progressive approximations. We also provide uniqueness proofs for the discrete cases.

AB - We discuss the topic of selecting optimal orthonormal bases for representing classes of signals defined either through statistics or via some deterministic characterizations, or combinations of the two. In all cases, the best bases result from spectral analysis of a Hermitian matrix that summarizes the prior information we have on the signals we want to represent, achieving optimal progressive approximations. We also provide uniqueness proofs for the discrete cases.

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U2 - 10.1016/j.crma.2016.10.002

DO - 10.1016/j.crma.2016.10.002

M3 - مقالة

SN - 1631-073X

VL - 354

SP - 1155

EP - 1167

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 12

ER -

Best bases for signal spaces

Abstract

All Science Journal Classification (ASJC) codes

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