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One of the properties mentioned in the literature about the lifting wavelet transform is that it can be applied on irregular meshes or grids (i.e. not equally spaced samples); but I don't seem to see that as an option in LiftingWaveletTransform. Any ideas on how to do that using Mathematica's wavelet analysis tools?

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Construct an "irregular grid" with a vertical discontinuity:

a = {{ConstantArray[0, {3, 3}], ConstantArray[1, {3, 5}]}, {ConstantArray[0, {5, 3}], 
   ConstantArray[1, {5, 5}]}}

Use ArrayFlatten to get a rectangular matrix:

b = ArrayFlatten@a

WaveletMatrixPlot[LiftingWaveletTransform[b]]

enter image description here

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  • $\begingroup$ Thanks @eldo, but b is just a {8,8} array and, therefore, representing a signal/function in a regular grid of $(i/8,j/8)$ points, that is not irregular. $\endgroup$ – carlosayam Jun 22 '14 at 19:47

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