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{{Orphan|date=November 2015}}
[[Wavelet]]s are often used to analyse piece-wise smooth signals.<ref>{{cite book|last1=Mallat|first1=Stéphane|title=A Wavelet Tour of Signal Processing|date=2008|publisher=Academic Press}}</ref> Wavelet coefficients can efficiently represent a signal which has led to data compression algorithms using wavelets.<ref>{{cite book |doi=10.1109/DCC.1991.213386|isbn=978-0-8186-9202-4|chapter=Data compression using wavelets: Error, smoothness and quantization|title=[1991] Proceedings. Data Compression Conference|pages=186–195|year=1991|last1=Devore|first1=R.A.|last2=Jawerth|first2=B.|last3=Lucier|first3=B.J.|chapter-url=https://www.semanticscholar.org/paper/8b93bc5d02cc102b82c17d3db9c98909275d8132}}</ref> Wavelet analysis is extended for [[multidimensional signal processing]] as well. This article introduces a few methods for wavelet synthesis and analysis for multidimensional signals. There also occur challenges such as directivity in multidimensional case.
== Multidimensional separable Discrete Wavelet Transform (DWT) ==
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== Multidimensional Complex Wavelet Transform==
Similar to the 1-D complex wavelet transform,<ref name=kingsbury>{{cite journal|last1=Kingsbury|first1=Nick|title=Complex Wavelets for Shift Invariant Analysis and Filtering of Signals|journal= Applied and Computational Harmonic Analysis|date=2001|volume=10|issue=3|pages=234–253|doi=10.1006/acha.2000.0343|url=http://www.idealibrary.com}}</ref> tensor products of complex wavelets are considered to produce complex wavelets for multidimensional signal analysis. With further analysis it is seen that these complex wavelets are oriented.<ref name=IEEEmag>{{cite journal|last1=Selesnick|first1=Ivan|last2=Baraniuk|first2=Richard|last3=Kingsbury|first3=Nick|title=The Dual-Tree Complex Wavelet Transform|journal=IEEE Signal Processing Magazine|volume=22|issue=6|date=2005|pages=123–151|
===Implementation of multidimensional (M-D) dual tree CWT ===
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{{math| H<sub>x</sub> H<sub>y</sub> {ψ(x)<sub>h</sub>ψ(y)<sub>h</sub>} {{=}} ψ(x)<sub>g</sub>ψ(y)<sub>g</sub> }}
For the 2-D case, this is named dual tree '''[[quaternion]] Wavelet Transform (QWT)'''.<ref>{{cite journal|last1=Lam Chan|first1=Wai|last2=Choi|first2=Hyeokho|last3=Baraniuk|first3=Richard|title=Coherent Multiscale Image Processing Using Dual-Tree Quaternion Wavelets|journal=IEEE Transactions on Image Processing|volume=17|issue=7|pages=1069–1082|date=2008|doi=10.1109/TIP.2008.924282|pmid=18586616|bibcode=2008ITIP...17.1069C|url=https://www.semanticscholar.org/paper/c7fd84b91df62e895c85d8afbcae76a0f7af0908}}</ref>
The total redundancy in M-D is {{math|2<sup>m</sup>}} tight frame.
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