A Bevy of Novel Interpolating Kernels for the Shannon Reconstruction of High-Bandpass Images

✍ Scribed by Salvatore Lanzavecchia; Pier Luigi Bellon

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 684 KB
• Volume: 6
• Category: Article
• ISSN: 1047-3203
• DOI: 10.1006/jvci.1995.1011

✦ Synopsis

A Shannon reconstruction of the values of sampled (n)-dimensional functions can be performed by a moving window technique (MWSR) with no truncation errors, provided that the window is regarded as a complete sampling interval. Each reconstructed point of the function is obtained by convoluting the samples with an interpolating kernel. The present paper demonstrates the mathematical derivation of a bevy of novel interpolating kernels and discusses their bandpass properties on the basis of precise quantitative data. Compared to linear interpolation and cubic spline algorithms, the novel kernels yield superior results in terms of bandpass. This makes possible to reduce the oversampling of functions that need to be interpolated. Some applications of the MWSR, based on the properties of the novel kernels, are discussed, especially with regard to problems involving transformations of coordinates. O (1995 \mathrm{Aca}). demic Press, Inc.