Wavelet for multidimensional signals analysis: Difference between revisions

Revision as of 05:34, 11 December 2015

Revision as of 05:54, 11 December 2015

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Similarly, by considering {{math| ψ₂(x,y) {{=}} ψ(x)ψ(y)^*}}, a wavelet oriented at {{math|45^o}} is obtained. To obtain 4 more oriented real wavelets, {{math|φ(x)ψ(y)}}, {{math|ψ(x)φ(y)}}, {{math|φ(x)ψ(y)^*}} and {{math|ψ(x)φ(y)^*}} are considered.

ForThe implementation of thiscomplex 2oriented dual tree structure is done as follows: Two separable 2-D DWTs are implemented in parallel areusing the filterbank structure as in the previous neededsection. Then, the appropriate sum and difference of different subbands (LL, LH, HL, HH) give oriented wavelets, a total of 6 in all.

[[Image:Wavelet orientation.jpg|framed|none|The figure shows the Fourier support of all 6 oriented wavelets obtained by a 2-D real oriented dual tree CWT]]

Similarly, in 3-D, 4 separable 3-D DWTs in parallel are needed and a total of 28 oriented wavelets are obtained.