Wavelet for multidimensional signals analysis: Difference between revisions

Revision as of 01:12, 13 November 2015

Revision as of 01:14, 13 November 2015

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===Disadvantage of M-D CWT===

Although M-D CWT provides one with oriented wavelets, these orientations are only appropriate to represent the orientation along {{math|m-1}} dimension of a signal with {{math|m}} dimensions. When singularities in [[Manifolds|manifold]]<ref>{{cite book|last1=Boothby|first1=W|title=An Introduction to Differentiable Manifolds and Riemannian Geometry|date=2003|publisher=Academic|___location=San Diego}}</ref> of lower dimensions are considered, such as a bee moving in a straight line in the 4-D space-time, we need oriented wavelets that are smooth in the direction of the manifold and change rapidly in the direction normal to it are needed. A new transform, Hypercomplex Wavelet transform was developed in order to address this issue.

==Hypercomplex Wavelet Transform==