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A Theory of Lossy Compression for Individual Data | Nikolai K. Vereshchagin
; Paul M.B. Vitanyi
; | Date: |
7 Nov 2004 | Subject: | Information Theory ACM-class: E.4, H.1.1 | cs.IT | Affiliation: | Moscow State Univ.), Paul M.B. Vitanyi (CWI and University of Amsterdam | Abstract: | We develop rate-distortion theory for individual data with respect to general distortion measures, that is, a theory of lossy compression of individual data. This is applied to Euclidean distortion, Hamming distortion, Kolmogorov distortion, and Shannon-Fano distortion. We show that in all these cases for every function satisfying the obvious constraints there are data that have this function as their individual rate-distortion function. Shannon’s distortion-rate function over a random source is shown to be the pointswise asymptotic expectation of the individual distortion-rate functions we have defined. The great differences in the distortion-rate functions for individual non-random (that is, the aspects important to lossy compression) data we established were previously invisible and obliterated in the Shannon theory. The techniques are based on Kolmogorov complexity. | Source: | arXiv, cs.IT/0411014 | Services: | Forum | Review | PDF | Favorites |
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