Cardinal B-spline dictionaries on a compact interval

Miroslav Andrle; Laura Rebollo-Neira

doi:10.1016/j.acha.2005.01.001

Cardinal B-spline dictionaries on a compact interval

Miroslav Andrle, Laura Rebollo-Neira^*

^*Corresponding author for this work

Aston University

Research output: Contribution to journal › Letter, comment/opinion or interview › peer-review

Abstract

A prescription for constructing dictionaries for cardinal spline spaces on a compact interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a compact interval can be spanned by dictionaries of cardinal B-spline functions of broader support than the corresponding basis functions.

Original language	English
Pages (from-to)	336-346
Number of pages	11
Journal	Applied and Computational Harmonic Analysis
Volume	18
Issue number	3
DOIs	https://doi.org/10.1016/j.acha.2005.01.001
Publication status	Published - 1 May 2005

Keywords

B-spline dictionaries
Cardinal spline spaces
Non-linear approximation
Sparse representation

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10.1016/j.acha.2005.01.001

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AB - A prescription for constructing dictionaries for cardinal spline spaces on a compact interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a compact interval can be spanned by dictionaries of cardinal B-spline functions of broader support than the corresponding basis functions.

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KW - Cardinal spline spaces

KW - Non-linear approximation

KW - Sparse representation

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Cardinal B-spline dictionaries on a compact interval

Abstract

Keywords

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