Wavelet for multidimensional signals analysis: Difference between revisions

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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 as [http://www.uio.no/studier/emner/matnat/math/MAT-INF2360/v12/tensorwavelet.pdf<ref>{{cite web|title=Tensor products in a wavelet setting|url=http://www.uio.no/studier/emner/matnat/math/MAT-INF2360/v12/tensorwavelet.pdf|website=University of Oslo|date=2012}}</ref>]

{{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) }}}