DocumentCode :
851658
Title :
B-spline signal processing. I. Theory
Author :
Unser, Michael ; Aldroubi, Akram ; Eden, Murray
Volume :
41
Issue :
2
fYear :
1993
fDate :
2/1/1993 12:00:00 AM
Firstpage :
821
Lastpage :
833
Abstract :
The use of continuous B-spline representations for signal processing applications such as interpolation, differentiation, filtering, noise reduction, and data compressions is considered. The B-spline coefficients are obtained through a linear transformation, which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering. The same property also applies for the indirect B-spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines. The filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for B-splines of any order. Applications to differentiation, filtering, smoothing, and least-squares approximation are examined. The extension of such operators for higher-dimensional signals such as digital images is considered
Keywords :
data compression; differentiation; digital filters; filtering and prediction theory; image processing; interference suppression; interpolation; least squares approximations; signal processing; splines (mathematics); B-spline coefficients; B-spline signal processing; data compressions; differentiation; digital filters; digital images; filtering; higher-dimensional signals; interpolation; least squares splines; linear filtering; linear transformation; noise reduction; smoothing splines; transfer functions; Data compression; Filtering; Interpolation; Least squares approximation; Maximum likelihood detection; Noise reduction; Nonlinear filters; Signal processing; Smoothing methods; Spline;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.193220
Filename :
193220
Link To Document :
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