On the concept of best achievable compression ratio for lossy image coding

The trade-off between image fidelity and coding rate is reached with several techniques, but all of them require an ability to measure distortion. The problem is that finding a general enough measure of perceptual quality has proven to be an elusive goal. Here, we propose a novel technique for deriving an optimal compression ratio for lossy coding based on the relationship between information theory and the problem of testing hypotheses. The best achievable compression ratio determines a boundary between achievable and non-achievable regions in the trade-off between source fidelity and coding rate. The resultant performance bound is operational in that it is directly achievable by a constructive procedure, as suggested in a theorem that states the relationship between the best achievable compression ratio and the Kullback–Leibler information gain. As an example of the proposed technique, we analyze the effects of lossy compression at the best achievable compression ratio on the identification of breast cancer microcalcifications.