Editing Discrete cosine transform (section)

===Multidimensional DCT===
{{See also|ZPEG}}

Multidimensional DCTs (MD DCTs) have several applications, mainly 3-D DCTs such as the 3-D DCT-II, which has several new applications like Hyperspectral Imaging coding systems,<ref name="appDCT">{{Citation |first1=G. P. |last1=Abousleman |first2=M. W. |last2=Marcellin |first3=B. R. |last3=Hunt |title=Compression of hyperspectral imagery using 3-D DCT and hybrid DPCM/DCT |journal=IEEE Trans. Geosci. Remote Sens. |date=January 1995 |volume=33 |issue=1 |pages=26–34 |doi=10.1109/36.368225|bibcode=1995ITGRS..33...26A }}</ref> variable temporal length 3-D DCT coding,<ref name="app2DCT">{{Citation |first1=Y. |last1=Chan |first2=W. |last2=Siu |title= Variable temporal-length 3-D discrete cosine transform coding |journal=IEEE Trans. Image Process. |date=May 1997 |volume=6 |issue=5 |pages=758–763 |doi=10.1109/83.568933|pmid=18282969 |bibcode=1997ITIP....6..758C |hdl=10397/1928 |url=http://www.en.polyu.edu.hk/~wcsiu/paper_store/Journal/1997/1997_J3-IEEE-Chan%26Siu.pdf |citeseerx=10.1.1.516.2824 }}</ref> [[video coding]] algorithms,<ref name="app3DCT">{{Citation |first1=J. |last1=Song |first2=Z. |last2=SXiong |first3=X. |last3=Liu |first4=Y. |last4=Liu |title= An algorithm for layered video coding and transmission| journal= Proc. Fourth Int. Conf./Exh. High Performance Comput. Asia-Pacific Region |volume=2 |pages=700–703}}</ref> adaptive video coding<ref name="app4DCT">{{Citation |first1=S.-C |last1=Tai |first2=Y. |last2=Gi |first3=C.-W. |last3=Lin |title= An adaptive 3-D discrete cosine transform coder for medical image compression |journal= IEEE Trans. Inf. Technol. Biomed. |date=September 2000 |volume=4 |issue=3 |pages=259–263 |doi=10.1109/4233.870036|pmid=11026596 |s2cid=18016215 }}</ref> and 3-D Compression.<ref name="app5DCT">{{Citation |first1=B. |last1=Yeo |first2=B. |last2=Liu |title= Volume rendering of DCT-based compressed 3D scalar data |journal=IEEE Transactions on Visualization and Computer Graphics |date=May 1995 |volume=1 |pages=29–43 |doi=10.1109/2945.468390}}</ref> Due to enhancement in the hardware, software and introduction of several fast algorithms, the necessity of using MD DCTs is rapidly increasing. [[#DCT-IV|DCT-IV]] has gained popularity for its applications in fast implementation of real-valued polyphase filtering banks,<ref>{{cite book| doi=10.1109/ISCAS.2000.856261 | chapter=Perfect reconstruction modulated filter banks with sum of powers-of-two coefficients | title=2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353) | year=2000 | last1=Chan | first1=S.C. | last2=Liu | first2=W. | last3=Ho | first3=K.I. | volume=2 | pages=73–76 | hdl=10722/46174 | isbn=0-7803-5482-6 | s2cid=1757438 }}</ref> lapped orthogonal transform<ref>{{cite journal |last1=Queiroz |first1=R. L. |last2=Nguyen |first2=T. Q. |title=Lapped transforms for efficient transform/subband coding |journal=IEEE Trans. Signal Process. |date=1996 |volume=44 |issue=5 |pages=497–507}}</ref>{{sfn|Malvar|1992}} and cosine-modulated wavelet bases.<ref>{{cite journal |last1=Chan |first1=S. C. |last2=Luo |first2=L. |last3=Ho |first3=K. L. |title=M-Channel compactly supported biorthogonal cosine-modulated wavelet bases |journal=IEEE Trans. Signal Process. |date=1998 |volume=46 |issue=2 |pages=1142–1151|doi=10.1109/78.668566 |bibcode=1998ITSP...46.1142C |hdl=10722/42775 |hdl-access=free }}</ref>