Set theoretic compression with an application to image coding

We discuss the concept of set theoretic compression where the input signal is implicitly encoded by the specification of a set which contains it, rather than an estimate which approximates it. This approach assumes the reconstruction of an estimate from the encoded set information only at the decoder side. We explain the motivations of this approach for high signal compression and encoding simplification, and the implication of more complex decoding. We then present the tools to support the approach. We finally show a demonstration of this approach in a particular application of image coding.< >