Geometric Sampling of Images, Vector Quantization and Zador's Theorem
Résumé
We present several consequences of the geometric approach to image sampling and reconstruction we have previously introduced. We single out the relevance of the geometric method to the vector quantization of images and, more important, we give a concrete and candidate for the optimal embedding dimension in Zador's Thorem. An additional advantage of our approach is that that this provides a constructive proof of the aforementioned theorem, at least in the case of images. Further applications are also briefly discussed.
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