descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Other literature type 01 Jan 2014 English Publisher:Springer Netherlands

Authors: Amir Averbuch; Valery A. Zheludev; Pekka Neittaanmäki;

doi: 10.1007/978-94-017-8926-4_15 , 10.1007/978-3-319-22303-2_11

Biorthogonal Wavelet Transforms

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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.

Related Organizations

Tel Aviv University
Israel
University of Jyväskylä
Finland

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