A method of compressing an image is described in which digital data signals in a 2-dimensional images are formed into an image data pyramid with a number of layers and each layer is processed to give a compressed encoding in an ordered list. The encoding with the largest quality gain factor is selected first and added to a compressed representation of the data array. This is repeated for the next largest gain factor and so on until a predetermined maximum is reached. Each layer of the image data pyramid corresponds to different frequency bands, the vector quantizations of these layers will only minimally interfere with one another. This allows a simple ordering of all possible gain contributions made by the compressed encodings, to the compressed representation. This in turn allows a straightforward selection of the compressed encodings having the largest quality gain factors, for compiling the compressed representation of the image.