Spline and Spline Wavelet Methods with Applications to Signal and Image Processing by Amir Z. Averbuch Pekka Neittaanmäki & Valery A. Zheludev

Author:Amir Z. Averbuch, Pekka Neittaanmäki & Valery A. Zheludev
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Amir Z. Averbuch (Corresponding author)

Email: [email protected]

Pekka Neittaanmäki

Email: [email protected]

Valery A. Zheludev

Email: [email protected]

Abstract

Wavelets in the polynomial and discrete spline spaces were introduced in Chaps. 8 and 10, respectively. In both cases, the wavelets’ design and implementation of the transforms were associated with perfect reconstruction (PR) filter banks. In this chapter, those associations are discussed in more detail. Biorthogonal wavelet bases generated by PR filter banks are investigated and a few examples of compactly supported biorthogonal wavelets are presented. Conditions for filters to restore and annihilate sampled polynomials are established (discrete vanishing moment property). In a sense, the material of this chapter is introductory to Chap. 12, where splines are used as a source for (non-spline) wavelets’ design.

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