Principal shift-invariant spaces with extra invariance nearest to observed data

Akram Aldroubi; Ilya Krishtal; Romain Tessera; Haichao Wang

doi:10.1007/s13348-011-0047-7

Principal shift-invariant spaces with extra invariance nearest to observed data

Akram Aldroubi
, Ilya Krishtal
, Romain Tessera
, Haichao Wang

Vanderbilt University
Northern Illinois University
Ecole Normale Supérieure de Lyon

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

Given a set of functions F={f ₁,...,f _m} ⊂ L ² (ℝ) we construct a principal shift-invariant space V nearest to F in the sense that V minimizes the expression among all the principal shift-invariant spaces with an orthonormal generator which are also translation invariant, or among all the principal shift-invariant spaces with an orthonormal generator which are also 1/2ℤ-invariant for some fixed n ∈ ℕ.

langue originale	Anglais
Pages (de - à)	393-401
Nombre de pages	9
journal	Collectanea Mathematica
Volume	63
Numéro de publication	3
Les DOIs	https://doi.org/10.1007/s13348-011-0047-7
état	Publié - 1 sept. 2012
Modification externe	Oui

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10.1007/s13348-011-0047-7

Contient cette citation

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abstract = "Given a set of functions F=\{f 1,...,f m\} ⊂ L 2 (ℝ) we construct a principal shift-invariant space V nearest to F in the sense that V minimizes the expression among all the principal shift-invariant spaces with an orthonormal generator which are also translation invariant, or among all the principal shift-invariant spaces with an orthonormal generator which are also 1/2ℤ-invariant for some fixed n ∈ ℕ.",

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N2 - Given a set of functions F={f 1,...,f m} ⊂ L 2 (ℝ) we construct a principal shift-invariant space V nearest to F in the sense that V minimizes the expression among all the principal shift-invariant spaces with an orthonormal generator which are also translation invariant, or among all the principal shift-invariant spaces with an orthonormal generator which are also 1/2ℤ-invariant for some fixed n ∈ ℕ.

AB - Given a set of functions F={f 1,...,f m} ⊂ L 2 (ℝ) we construct a principal shift-invariant space V nearest to F in the sense that V minimizes the expression among all the principal shift-invariant spaces with an orthonormal generator which are also translation invariant, or among all the principal shift-invariant spaces with an orthonormal generator which are also 1/2ℤ-invariant for some fixed n ∈ ℕ.

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KW - Least square

KW - Shift-invariant spaces

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DO - 10.1007/s13348-011-0047-7

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Principal shift-invariant spaces with extra invariance nearest to observed data

Résumé

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