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de Oliveira, H. M.; Vermehren, V. V.; Cintra, R. J.

Multi-dimensional wavelets for scalable image decomposition: orbital wavelets. (English) Zbl 1457.42051

Int. J. Wavelets Multiresolut. Inf. Process. 18, No. 5, Article ID 2050038, 11 p. (2020).
The paper deals with a 2-D continuous wavelet transform. The authors propose to use the following nonseparable choice of wavelet transform \begin{gather*} \widehat{\varphi}_{LL}(x,\,y) = \frac{1}{\sqrt{2}} \left(\varphi^{\ast}(x) \varphi(y) +\varphi^{\ast}(y) \varphi(x)\right), \\ \widehat{\psi}_{LH}(x,\,y) = \frac{1}{\sqrt{2}} \left(\varphi(x) \psi(y) -\varphi(y) \psi(x)\right),\\ \widehat{\psi}_{HL}(x,\,y) = - \widehat{\psi}_{LH}(x,\,y),\\ \widehat{\psi}_{HH}(x,\,y) = \frac{1}{\sqrt{2}} \left(\psi^{\ast}(x) \psi(y) -\psi^{\ast}(y) \psi(x)\right), \end{gather*} where \(\varphi\) and \(\psi\) denote a 1-D scaling function and a 1-D wavelet function respectively. (The author’s notation is kept.) The suggested choice is illustrated by a picture of image decomposition.
Reviewer: Elena Lebedeva (Saint Petersburg)

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
65T60 Numerical methods for wavelets
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
70M99 Orbital mechanics

Keywords:

2D wavelets; anti-symmetric wavelets; orthogonal wavelets; image analysis

Software:

DT-CWT; Wavelet Toolbox
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Full Text: DOI arXiv

References:

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