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Improving distribution and flexible quantization for DCT coefficients

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Document pages: 11 pages

Abstract: While it is a common knowledge that AC coefficients of Fourier-relatedtransforms, like DCT-II of JPEG image compression, are from Laplacedistribution, there was tested more general EPD (exponential powerdistribution) $ rho sim exp(-(|x- mu| sigma)^{ kappa})$ family, leading tomaximum likelihood estimated (MLE) $ kappa approx 0.5$ instead of Laplacedistribution $ kappa=1$ - such replacement gives $ approx 0.1$ bits value meansavings (per pixel for grayscale, up to $3 times$ for RGB).There is also discussed predicting distributions (as $ mu, sigma, kappa$parameters) for DCT coefficients from already decoded coefficients in thecurrent and neighboring DCT blocks. Predicting values $( mu)$ from neighboringblocks allows to reduce blocking artifacts, also improve compression ratio -for which prediction of uncertainty width $ sigma$ alone provides much larger$ approx 0.5$ bits value mean savings opportunity (often neglected).Especially for such continuous distributions, there is also discussedquantization approach through optimized continuous emph{quantization densityfunction} $q$, which inverse CDF (cumulative distribution function) $Q$ onregular lattice $ {Q^{-1}((i-1 2) N):i=1 ldots N }$ gives quantization nodes -allowing for flexible inexpensive choice of optimized (non-uniform)quantization - of varying size $N$, with rate-distortion control. Optimizing$q$ for distortion alone leads to significant improvement, however, at cost ofincreased entropy due to more uniform distribution. Optimizing both turns outleading to nearly uniform quantization here, with automatized tail handling.

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