Fast Computation by Subdivision of Multidimensional Splines and Their Applications
Averbuch, A., Neittaanmäki, P., Shabat, G., & Zheludev, V. (2016). Fast Computation by Subdivision of Multidimensional Splines and Their Applications. Pure and Applied Functional Analysis, 1(3), 309-341. http://www.ybook.co.jp/online2/oppafa/vol1/p309.html
Published inPure and Applied Functional Analysis
© 2016 Yokohama Publishers. This is a final draft version of an article whose final and definitive form has been published by Yokohama Publishers. Published in this repository with the kind permission of the publisher.
We present theory and algorithms for fast explicit computations of uni- and multi-dimensional periodic splines of arbitrary order at triadic rational points and of splines of even order at diadic rational points. The algorithms use the forward and the inverse Fast Fourier transform (FFT). The implementation is as fast as FFT computation. The algorithms are based on binary and ternary subdivision of splines. Interpolating and smoothing splines are used for a sample rate convertor such as resolution upsampling of discrete-time signals and digital images and restoration of decimated images that were contaminated by noise. The performance of the rate conversion based spline is compared with the performance of the rate conversion by prolate spheroidal wave functions.
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