Discrete Cosine Transform (DCT). Furht, B., editor In Encyclopedia of Multimedia, pages 186–188. Springer US, 2008. 00000
DefinitionDiscrete Cosine Transform is a technique applied to image pixels in spatial domain in order to transform them into a frequency domain in which redundancy can be identified.In JPEG compression [1], image is divided into 8 × 8 blocks, then the two-dimensional Discrete Cosine Transform (DCT) is applied to each of these 8 × 8 blocks. In JPEG decompression, the Inverse Discrete Cosine Transform (IDCT) is applied to the 8 × 8 DCT coefficient blocks. DCT and IDCT are defined as follows:DCT:F(u,v)=14C(u)C(v)∑i=07∑j=07f(i,j)cos((2i+1)uπ/16)cos((2j+1)vπ/16)DCT:F(u,v)=14C(u)C(v)∑i=07∑j=07f(i,j)cos⁡((2i+1)uπ/16)cos⁡((2j+1)vπ/16)\textbackslashbegin\array\ \*\20\l\DCT: &\textbackslash\textbackslash & F(u,v) = \1\textbackslashover4\C(u)C(v)\textbackslashsum\textbackslashlimits_\i = 0\\textasciicircum7 \textbackslashsum\textbackslashlimits_\j = 0\\textasciicircum7 f(i,j) \textbackslash\textbackslash &\textbackslashcos ((2i + 1)u\textbackslashpi /16)\textbackslashcos ((2j + 1)v\textbackslashpi /16)\textbackslashend\array\IDCT:f(i,j)=14∑u=07∑v=07C(u)C(v)F(u,v)cos((2i+1)uπ/16)cos((2j+1)vπ/16)IDCT:f(i,j)=14∑u=07∑v=07C(u)C(v)F(u,v)cos⁡((2i+1)uπ/16)cos⁡((2j+1)vπ/16)\textbackslashbegin\array\ \*\20\l\IDCT: & \textbackslash\textbackslash & f(i,j) = \1\textbackslashover 4\\textbackslashsum\textbackslashlimits_\u = 0\\textasciicircum7 \textbackslashsum\textbackslashlimits_\v = 0\\textasciicircum7 C(u)C(v)F(u,v) \textbackslash\textbackslash &\textbackslashcos ((2i + 1)u \textbackslashpi /16)\textbackslashcos ((2j + 1)v \textbackslashpi /16) \textbackslashend\array\ where f(i, j) and F(u, ν) are respectively the pixel value and the DCT coefficient, and ...
@incollection{furht_discrete_2008-1,
title = {Discrete {Cosine} {Transform} ({DCT})},
}