文章基本信息

标题：Trigonometric Polynomial Interpolation of Images
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作者：Thibaud Briand
期刊名称：Image Processing On Line
电子版ISSN：2105-1232
出版年度：2019
卷号：9
页码：291-316
DOI：10.5201/ipol.2019.273
出版社：Image Processing On Line
摘要：For 1D and 2D signals, the Shannon-Whittaker interpolation with periodic extension can be formulated as a trigonometric polynomial interpolation (TPI). In this work, we describe and discuss the theory of TPI of images and some of its applications. First, the trigonometric polynomial interpolators of an image are characterized and it is shown that there is an ambiguity as soon as one size of the image is even. Three classical choices of interpolator for real-valued images are presented and cases where they coincide are pointed out. Then, TPI is applied to the geometric transformation of images, to up-sampling and to down-sampling. General results are expressed for any choice of interpolator but more details are given for the three proposed ones. It is proven that the well-known DFT-based computations have to be slightly adapted.
关键词：interpolation; trigonometric polynomial; trigonometric polynomial interpolation; discrete Fourier transform (DFT); Non;equispaced fast Fourier transform (NFFT)