On the optimal choice of quality metric in image compression

There exist many, different lossy compression methods, and most of these methods have several tunable parameters. In different situations, different methods lead to different quality reconstruction, so it is important to select, in each situation, the best compression method. A natural idea is to select the compression method for which the average value of some metric d(I, I˜) is the smallest possible. The question is then: which quality metric should we choose? In this paper, we show that under certain reasonable symmetry conditions, L^p metrics d(I, I˜) = ∫ |I(x)-I˜(x)|^pdx are the best, and that the optimal value of p can be selected depending on the expected relative size r of the informative part of the image