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Fourier series spectral coefficients correlation for shifted blocks


Y.S. Radchenko, S.V. Milyaev

Modern communication systems, computer networks and other information transmission systems should provide interchange of multimedia data in real time. Here arises the problem of image and video compression. Usually it is necessary to perform lossy data compression, when the most methods do the following operations: orthogonal transform, spectral coefficients quantization and entropy coding. Correlation coefficient between spectral mods helps to evaluate how optimal the selected orthogonal basis in terms of spectral coefficients decorrelation. During intra-frame prediction, which widely used in modern algorithms for image and video compression, knowledge of the correlation between spectral coefficients of neighbor blocks provide more efficient prediction. Knowledge of correlation of spectrum mods of orthogonal basis is necessary for evaluation of information measure and maximum image compression coefficient. In this paper the problem of correlation coefficient estimation for Fourier series spectral coefficients of shifted blocks from some signal realization for discrete and continuous signals is solved. It is shown that in single block odd and even spectral mods are not correlated to each other and only closest odd or even spectral mods have non-zero correlation. Numerical estimates of correlation coefficient of spectral coefficients for widely used in image in video compression algorithms orthogonal transforms such as discrete cosine transform (DCT), integer DCT and discrete Tchebyshev transform (GDCT), which uses irregular sample grid are performed. It is shown, that correlation of higher spectral mods between neighbor blocks is close to zero. Correlation of DC spectrum coefficients is considerable only when the value of inter-pixel correlation is higher than 0.9. It is shown that GDCT provides higher decorrelation of spectral coefficients compare to DCT. Performed estimates for correlation coefficient of spectral coefficients between shifted blocks provide evaluation of possibility using spectral mods for motion estimation.

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