Abstract
This article examines a notion of finite-dimensional wavelet systems on \({\mathbb{T}}^{2}\), which employ a dilation operation induced by the Quincunx matrix. A theory of multiresolution analysis (MRA) is presented which includes the characterization and construction of MRA scaling functions in terms of low-pass filters. Orthonormal wavelet systems are constructed for any given MRA. Two general examples, based upon the classical Shannon and Haar wavelets, are presented and the approximation properties of the associated systems are studied.
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References
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Hoover, K.R., Johnson, B.D. (2011). Quincunx Wavelets on \({\mathbb{T}}^{2}\) . In: Cohen, J., Zayed, A. (eds) Wavelets and Multiscale Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-8095-4_4
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DOI: https://doi.org/10.1007/978-0-8176-8095-4_4
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Publisher Name: Birkhäuser Boston
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Online ISBN: 978-0-8176-8095-4
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