Editing Wavelet (section)

== History ==
The development of wavelets can be linked to several separate trains of thought, starting with [[Alfréd Haar]]'s work in the early 20th century. Later work by [[Dennis Gabor]] yielded [[Gabor atom]]s (1946), which are constructed similarly to wavelets, and applied to similar purposes.

Notable contributions to wavelet theory since then can be attributed to [[George Zweig]]’s discovery of the [[continuous wavelet transform]] (CWT) in 1975 (originally called the cochlear transform and discovered while studying the reaction of the ear to sound),<ref>{{cite web |last=Weisstein |first=Eric W. |title=Zweig, George -- from Eric Weisstein's World of Scientific Biography |url=https://scienceworld.wolfram.com/biography/Zweig.html |access-date=2021-10-20 |website=scienceworld.wolfram.com |language=en}}</ref> Pierre Goupillaud, [[Alex Grossmann]] and [[Jean Morlet]]'s formulation of what is now known as the CWT (1982), Jan-Olov Strömberg's early work on [[Strömberg wavelet|discrete wavelets]] (1983), the Le Gall–Tabatabai (LGT) 5/3-taps non-orthogonal filter bank with linear phase (1988),<ref>{{cite web |last1=Sullivan |first1=Gary |title=General characteristics and design considerations for temporal subband video coding |publisher=[[Video Coding Experts Group]] |website=[[ITU-T]] |date=8–12 December 2003 |url=https://www.itu.int/wftp3/av-arch/video-site/0312_Wai/VCEG-U06.doc |access-date=13 September 2019}}</ref><ref>{{cite book |last1=Bovik |first1=Alan C. |title=The Essential Guide to Video Processing |date=2009 |publisher=[[Academic Press]] |isbn=9780080922508 |page=355 |url=https://books.google.com/books?id=wXmSPPB_c_0C&pg=PA355}}</ref><ref>{{cite book |last1=Gall |first1=Didier Le |last2=Tabatabai |first2=Ali J. |title=ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing |chapter=Sub-band coding of digital images using symmetric short kernel filters and arithmetic coding techniques |date=1988 |pages=761–764 vol.2 |doi=10.1109/ICASSP.1988.196696|s2cid=109186495 }}</ref> [[Ingrid Daubechies]]' orthogonal wavelets with compact support (1988), [[Stephane Mallat|Stéphane Mallat]]'s non-orthogonal multiresolution framework (1989), [[Ali Akansu]]'s [[binomial QMF]] (1990), Nathalie Delprat's time-frequency interpretation of the CWT (1991), Newland's [[harmonic wavelet transform]] (1993), and [[set partitioning in hierarchical trees]] (SPIHT) developed by Amir Said with William A. Pearlman in 1996.<ref name="Said">{{cite journal |last1=Said |first1=Amir |last2=Pearlman |first2=William A. |title=A new fast and efficient image codec based on set partitioning in hierarchical trees |journal=IEEE Transactions on Circuits and Systems for Video Technology |volume=6 |pages=243–250 |date=June 1996 |issn=1051-8215 |doi=10.1109/76.499834 |issue=3}}</ref>

The [[JPEG 2000]] standard was developed from 1997 to 2000 by a [[Joint Photographic Experts Group]] (JPEG) committee chaired by Touradj Ebrahimi (later the JPEG president).<ref>{{cite book |last1=Taubman |first1=David |last2=Marcellin |first2=Michael |title=JPEG2000 Image Compression Fundamentals, Standards and Practice: Image Compression Fundamentals, Standards and Practice |date=2012 |publisher=[[Springer Science & Business Media]] |isbn=9781461507994 |url=https://books.google.com/books?id=y7HeBwAAQBAJ&pg=PA402}}</ref> In contrast to the DCT algorithm used by the original [[JPEG]] format, JPEG 2000 instead uses [[discrete wavelet transform]] (DWT) algorithms. It uses the [[Cohen-Daubechies-Feauveau wavelet|CDF]] 9/7 wavelet transform (developed by Ingrid Daubechies in 1992) for its [[lossy compression]] algorithm, and the Le Gall–Tabatabai (LGT) 5/3 discrete-time filter bank (developed by Didier Le Gall and Ali J. Tabatabai in 1988) for its [[lossless compression]] algorithm.<ref name="Unser">{{cite journal |last1=Unser |first1=M. |last2=Blu |first2=T. |title=Mathematical properties of the JPEG2000 wavelet filters |journal=IEEE Transactions on Image Processing |date=2003 |volume=12 |issue=9 |pages=1080–1090 |doi=10.1109/TIP.2003.812329 |url=https://pdfs.semanticscholar.org/6ed4/dece8b364416d9c390ba53df913bca7fb9a6.pdf |archive-url=https://web.archive.org/web/20191013222932/https://pdfs.semanticscholar.org/6ed4/dece8b364416d9c390ba53df913bca7fb9a6.pdf |url-status=dead |archive-date=2019-10-13 |pmid=18237979|bibcode=2003ITIP...12.1080U |s2cid=2765169 }}</ref> [[JPEG 2000]] technology, which includes the [[Motion JPEG 2000]] extension, was selected as the [[video coding standard]] for [[digital cinema]] in 2004.<ref>{{cite book |last1=Swartz |first1=Charles S. |title=Understanding Digital Cinema: A Professional Handbook |date=2005 |publisher=[[Taylor & Francis]] |isbn=9780240806174 |page=147 |url=https://books.google.com/books?id=tYw3ehoBnjkC&pg=PA147}}</ref>

=== Timeline ===
* First wavelet ([[Haar Wavelet|Haar's wavelet]]) by [[Alfréd Haar]] (1909)
* Since the 1970s: [[George Zweig]], [[Jean Morlet]], [[Alex Grossmann]]
* Since the 1980s: [[Yves Meyer]], [[Stéphane Mallat]], [[Ingrid Daubechies]], [[Ronald Coifman]], [[Ali Akansu]], [[Victor Wickerhauser]]
* Since the 1990s: Nathalie Delprat, Newland, Amir Said, William A. Pearlman, Touradj Ebrahimi, [[JPEG 2000]]