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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>{{citeCite book journal|last1doi =Lam Chan10.1109/ICASSP.2004.1326715|first1chapter =Wai|last2=Choi|first2=Hyeokho|last3=Baraniuk|first3=Richard Directional hypercomplex wavelets for multidimensional signal analysis and processing|title =DIRECTIONAL HYPERCOMPLEX2004 WAVELETSIEEE FORInternational MULTIDIMENSIONALConference SIGNALon ANALYSISAcoustics, ANDSpeech, PROCESSINGand Signal Processing|journalvolume =IEEE Icassp3|datepages = iii-996-9|year = 2004|volumelast1 =3 Wai Lam Chan|pageslast2 =996–999 Hyeokho Choi|urllast3 =http://citeseerx Baraniuk|first3 = R.istG.psu.edu/viewdoc/download?|isbn = 0-7803-8484-9}}</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> }}
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