Rate Distortion and Denoising of Individual Data Using Kolmogorov Complexityстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:We examine the structure of families of distortion balls from the perspective of Kolmogorov complexity. Special attention is paid to the canonical rate-distortion function of a source word which returns the minimal Kolmogorov complexity of all distortion balls containing that word subject to a bound on their cardinality. This canonical rate-distortion function is related to the more standard algorithmic rate-distortion function for the given distortion measure. Examples are given of list distortion, Hamming distortion, and Euclidean distortion. The algorithmic rate-distortion function can behave differently from Shannon's rate-distortion function. To this end, we show that the canonical rate-distortion function can and does assume a wide class of shapes (unlike Shannon's); we relate low algorithmic mutual information to low Kolmogorov complexity (and consequently suggest that certain aspects of the mutual information formulation of Shannon's rate-distortion function behave differently than would an analogous formulation using algorithmic mutual information); we explore the notion that low Kolmogorov complexity distortion balls containing a given word capture the interesting properties of that word (which is hard to formalize in Shannon's theory) and this suggests an approach to denoising.