Image compression allows the memory capacity of an image to be reduced so that it can be sent via a computer network or carried on a storage medium. This reduction in memory capacity must not significantly deteriorate the quality of the compressed image. The DCT (Discrete Cosine Transform) method is based on the Fourier transform. The image processing (compression) discussed in this book is based on a program written in MATLAB. To check the quality of the compression of the image, a decompression of the image is called by evaluating the rate of deterioration of its quality. The image is recovered but with a certain percentage of deterioration compared to its initial state. The compression work in this book is done on images of different sizes (Pizza and Cameraman images). The images processed by this program are JPG format images with a square matrix shape and they are displayed in grey level. In the future, we will extend this program to compress the images in colour and in a rectangular shape with a better quality.