What is it?
Transform the signal into a basis where most coefficients are tiny (cosine transforms, wavelets), quantize them coarsely where the eye or ear will not notice, and entropy-code the rest. Video adds motion compensation between frames.
Formulas
- DCT-II, the transform of JPEG (on 8×8 blocks)
The mathematics behind it
JPEG and MP3 use cosine transforms (DCT/MDCT), close relatives of Fourier series, then drop small coefficients.
JPEG 2000 and many medical/scientific image formats use wavelet transforms.
Fractal image compression (1990s) encoded images as self-similar maps; it was abandoned for transform coding.
This page has the essentials. A fuller treatment (intuition, formal definition, worked example) is on the way.