Set theoretic compression with an application to image coding

We show that the complete information that is available after an image has been encoded is not just an approximate quantized image version, but a whole set of consistent images that contains the original image by necessity. From this starting point, we develop a set of tools to design a new class of encoders for image compression, based on a set decomposition and recombination of the image features. As an initial validation, we show the results of an experiment where these tools are used to modify the encoding process of block discrete cosine transform (DCT) coding in order to yield less blocking artifacts.