Wavelet for multidimensional signals analysis: Difference between revisions

Revision as of 22:36, 10 December 2015

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== Multidimensional separable Discrete Wavelet Transform (DWT) ==

The [[Discrete wavelet transform]] is extended to the multidimensional case using the [[tensor product]] of well known 1-D wavelets.

In 2-D for example, the tensor product space for 2-D is decomposed into four tensor product vector spaces<ref name=Tensor_products>{{cite journal|last1=Kugarajah|first1=Tharmarajah|last2=Zhang|first2=Qinghua|title=Multidimensional wavelet frames|journal=IEEE Transactions on Neural NetworkNetworks|date=06November August 20021995|volume=6|issue=6|pages=1552 - 1556|doi=10.1109/72.471353|url=http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=471353&tag=1}}</ref> as

{{math| ( &phi;(x) ⨁ &psi;(x) ) ⊗ ( &phi;(y) ⨁ &psi;(y) ) {{=}} { &phi;(x)&phi;(y), &phi;(x)&psi;(y), &psi;(x)&phi;(y), &psi;(x)&psi;(y) }}}