14.1. Theoretical background
Data compression aims to reduce the volume of data to be transmitted, processed or recorded, without significant information loss. Although many other quality indices exist, the mean square error defined below will be considered in this chapter to compare the different data compression algorithms:
In the above equation, s is the original signal (1D or 2D) initial, ŝ stands for the compressed signal and Nd denotes the signal length (number of samples or number of pixels). Note that in the case of an image compression ŝ is not always the best solution from the human eye point of view. For example, the properties of the two-dimensional discrete Fourier transform are not adapted to the human vision system. Thus, it is replaced by the discrete cosine transform in compression schemes.
Most compression algorithms presented in this chapter are defined for the 2-D case (image compression). Compression algorithms for the 1-D case can be easily obtained as particular cases. An image is often cut up into blocks before performing its compression. Their sizes and forms depend on the processing speed, compression rate and memory organization. Furthermore, the spatial correlation of the gray levels, which is usually isotropic, also has to be taken into account. At present, the best trade-off is obtained for square blocks of 4×4 pixels.
The intensities of the pixels ...