Basic concepts
JPEG 2000. A wavelet-based digital picture compression format

The principle of digital image compression is based on the passage from a matrix of pixel luminosity values to a matrix of coefficients translating visual frequencies, i.e. pixel-to-pixel variations, making it possible to code more homogeneous "flat" zones or zones of detail. It is the analysis of this latter matrix that will eliminate redundancy and thus reduce the volume of data. Since this operation involves numbers and their relationships, two mathematical tools are used:

• DCT (Discrete Cosine Transform), based on Fourier analysis, analyzes and processes the image by blocks of pixels; it is used by almost all image compression formats (JPEG, MPEG, etc.);

• the DWT transform (Discrete Wavelet Transform ), which simultaneously analyzes and processes all the pixels in the image; it is used by JPEG 2000 and some...