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 journal|last1=Lam Chan|first1=Wai|last2=Choi|first2=Hyeokho|last3=Baraniuk|first3=Richard|title=DIRECTIONAL HYPERCOMPLEX WAVELETS FOR MULTIDIMENSIONAL SIGNAL ANALYSIS AND PROCESSING|journal=ICASSP|date=2004|volume=3|pages=996–999􀀓􀀐􀀚􀀛􀀓􀀖􀀐􀀛􀀗􀀛􀀗􀀐􀀜􀀒􀀓􀀗􀀓􀀐􀀚􀀛􀀓􀀖􀀐􀀛􀀗􀀛􀀗􀀐􀀜􀀒􀀓􀀗􀀓􀀐􀀚􀀛􀀓􀀖􀀐􀀛􀀗􀀛􀀗􀀐􀀜􀀒􀀓􀀗􀀓􀀐􀀚􀀛􀀓􀀖􀀐􀀛􀀗􀀛􀀗􀀐􀀜􀀒􀀓􀀗|url=http://citeseerx.ist.psu.edu/viewdoc/download?}}</ref> consists of standard DWT tensor and {{math|2<sup>m -1</sup>}} wavelets obtained from combining 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 as described 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> }}