COMPRESSION COEFFICIENT IN THE ANALYSIS OF NOISY TEXTS AND IMAGES

Oleksii Kravchuk, Oleh Kushnir

Abstract


Background. We analyze the compression coefficient S associated with the two versions of a Lempel–Ziv algorithm (LZA) as a quantitative characteristic of structural order in noisy or corrupted data, using a natural-language text and a digital image. To model a stochastically perturbed text or image, we randomize the linguistic elements of the former and add uncorrelated Gaussian noise to the latter or randomize its pixels.

Materials and Methods. A fiction text “Moby Dick” by H. Melville was randomized at the linguistic levels of sentences, words, and characters. The number of randomization cycles N varied in the range from 0 to 109. We also analyzed the red channel of an 8-bit image “Peppers” with the size M = 512×512. The Gaussian noise with the standard deviations σ changing in the range from 0 to 400 was added to the image. On the whole, 50 randomized and 50 noisy image versions were generated. To apply the LZA compression to the image, we unfolded it into a one-dimensional sequence of pixel intensities and processed the appropriate textual representation of the image as usual text.

Results and Discussion. The sentence-level randomization almost does not change the S value, because it remains intact the internal structures of words and sentences, while the LZA has a local character. The word-level randomization decreases S, whereas the character-level randomization leads to the largest S decrease and produces almost incompressible text files at the largest N. The results obtained with the two LZA-type versions differ slightly in the effect of sentence randomization on the compressibility. For the randomized images, the S value sharply decreases when N approaches the total pixel number M, and then reaches saturation. The strongest changes in S for the noisy images occur in the range of .

Conclusion. Our results demonstrate that the LZA compression coefficient is sensitive to the loss of local order in the noisy data of different types, either randomized texts or randomized and noisy images. Since the LZA is based on repetitions and local regularities in a symbolic sequence, a decrease in S indicates partial destruction of order caused by randomization or noise. Hence, the compression coefficient can, in principle, serve as a measure of disorder in both symbolic sequences and pixel grids and so can help in detecting noisy data.

Keywords: data compression, noisy data analysis, noise detection, randomization, natural language processing, image processing.


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DOI: http://dx.doi.org/10.30970/eli.35.3

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