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

Department of Mathematics
Vanderbilt University
Department of Mathematical Sciences
Northern Illinois University
Ecole Normale Supérieure de Lyon

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

11 Citations (Scopus)

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.

Original language	English
Pages (from-to)	393-401
Number of pages	9
Journal	Collectanea Mathematica
Volume	63
Issue number	3
DOIs	https://doi.org/10.1007/s13348-011-0047-7
Publication status	Published - 1 Sept 2012
Externally published	Yes

Keywords

1/2ℤ-invariance
Least square
Shift-invariant spaces

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10.1007/s13348-011-0047-7

Cite this

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

Abstract

Keywords

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