Wavelet for multidimensional signals analysis: Difference between revisions

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==Hypercomplex Wavelet Transform==
The dual tree '''Hypercomplex Wavelet Transform (HWT)''' developed in <ref name=DHWT>{{Cite book |doi = 10.1109/ICASSP.2004.1326715|chapter = Directional hypercomplex wavelets for multidimensional signal analysis and processing|title = 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing|volume = 3|pages = iii-996-9iii–996–9|year = 2004|last1 = Wai Lam Chan|last2 = Hyeokho Choi|last3 = Baraniuk|first3 = R.G.|isbn = 0-7803-8484-9|hdl = 1911/19796}}</ref> consists of a standard DWT tensor and {{math|2<sup>m -1</sup>}} wavelets obtained from combining the 1-D Hilbert transform of these wavelets along the n-coordinates. In particular a 2-D HWT consists of the standard 2-D separable DWT tensor and three additional components:
 
{{math| H<sub>x</sub> {&psi;(x)<sub>h</sub>&psi;(y)<sub>h</sub>} {{=}} &psi;(x)<sub>g</sub>&psi;(y)<sub>h</sub> }}