Transform Coding
Transform coding removes the redundancies (correlation) in an images by changing coordinate systems.
We can think of a cluster of pixels, for instance those in an 8 by 8 block, as a vector in
some high-dimensional space (64 dimension in this case). If we transform this matrix appropriately
we can discover that a otherwise random collection of numbers is, in fact, highly correlated.
One common transform basis function that you have seen if the Fourier Basis (FFT). However the Fourier
basis makes some assumptions that are not optimal for images.
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First, it assumes that the image tiles an infinite plane. This leads to a transform that
contains both even (cosine-like) and odd (sine-ike) components.
If we make copies of the images with various flips we can end up with a function that has only
even (cosine-like) components.
The resulting FFT will only have real parts. This transform is called the Cosine Transform.
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