3.5 Discrete Cosine Transform

Transform coding algorithms, generally speaking, operate as two-step processes. In the first step, a linear transformation of the original signal (separated into subblocks of N X N pels each) is performed, in which pixel space is mapped into transform space. In the second step, the transformed signal is compressed by quantizing each subblock of transform coefficients. The reconstruction operation involves performing an inverse transformation of each decoded transformed subblock. The function of the transformation operation is to make the transformed samples more independent than the original samples so that the subsequent operation of quantization may be done more efficiently.

The transformation operation itself does not provide compression; rather, it is a remapping of the signal into another domain in which compression can be achieved more effectively. Compression can be achieved for two reasons. First, not all of the transform domain coefficients need to be transmitted to achieve acceptable picture quantity. Second, most of the coefficients that are transmitted can be encoded with reduced precision without seriously affecting image quality.