Sampling Distortion Measures
نویسندگان
چکیده
This paper is motivated by the following problem. Consider an image we want to compress. The appropriate distortion measure with respect to which we compress the image is specified by the human visual system. This distortion measure can only be experimentally determined and our knowledge about it will hence be only partial. This leads us to consider the general problem of lossy source coding with partial knowledge about the distortion measure. More precisely, the distortion measure is only known at a number of sampling points. We describe several measures for the loss we incur through the lack of full knowledge of the true distortion measure, each with a different operational meaning. We give an asymptotically tight characterization of this loss in terms of three key parameters: The number of sampling points, the dimensionality of the source, and the smoothness assumptions on the distortion measure.
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