Rate Distortion and Denoising of Individual Data Using Kolmogorov Complexity

@article{Vereshchagin2010RateDA,
  title={Rate Distortion and Denoising of Individual Data Using Kolmogorov Complexity},
  author={Nikolai K. Vereshchagin and Paul M. B. Vit{\'a}nyi},
  journal={IEEE Transactions on Information Theory},
  year={2010},
  volume={56},
  pages={3438-3454}
}
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… CONTINUE READING