| Abstract: | Images take lot of computer space; in many practical situations, we cannot store all original images, we have to use compression. Moreover, in many such situations, compression ratio provided by even the best lossless compression is not sufficient, so we have to use lossy compression. In a lossy compression, the reconstructed image ? is, in general, different from the original image I. 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,?) 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(x)??(x)| p dx 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. |
