改进DCT系数的分布和灵活性quantization
Improving distribution and flexible quantization for DCT coefficients
摘要：
虽然众所周知，傅立叶相关变换的AC系数，如JPEG图像压缩的DCT-II，来自拉普拉斯分布，但测试了更一般的EPD（指数幂分布）$ρ\sim \exp(-(|x-μ|/σ)^κ)$族，导致最大似然估计（MLE）$κ\approx 0.5$而不是拉普拉斯分布$κ=1$ -这样的替换给出了$\approx 0.1$位/值平均节省（对于灰度，每像素，对于RGB，高达$3\times$）。还讨论了从当前和相邻DCT块中已经解码的系数预测DCT系数的分布（作为$μ, σ, κ$参数）。预测来自相邻块的值$(μ)$允许减少块效应，还提高压缩比-为此，单独预测不确定性/宽度$σ$提供大得多的$\approx 0.5$比特/值平均节省机会（经常被忽视）。特别是对于这样的连续分布，还讨论了通过优化的连续\emph{quantization density function} $q$的量化方法，其在规则网格$\{Q^{-1}((i-1/2)/N):i=1\ldots N\}$上的逆CDF（累积分布函数）$Q$给出具有速率失真控制的变化大小$N$的量化节点-允许优化（非均匀）量化的灵活廉价选择。优化$q$的失真单独导致显着的改善，然而，在增加熵的成本，由于更均匀的分布。优化这两个结果导致几乎均匀的量化，自动化的尾部处理。
英文摘要：
While it is a common knowledge that AC coefficients of Fourier-related transforms, like DCT-II of JPEG image compression, are from Laplace distribution, there was tested more general EPD (exponential power distribution) $ρ\sim \exp(-(|x-μ|/σ)^κ)$ family, leading to maximum likelihood estimated (MLE) $κ\approx 0.5$ instead of Laplace distribution $κ=1$ - such replacement gives $\approx 0.1$ bits/value mean savings (per pixel for grayscale, up to $3\times$ for RGB). There is also discussed predicting distributions (as $μ, σ, κ$ parameters) for DCT coefficients from already decoded coefficients in the current and neighboring DCT blocks. Predicting values $(μ)$ from neighboring blocks allows to reduce blocking artifacts, also improve compression ratio - for which prediction of uncertainty/width $σ$ alone provides much larger $\approx 0.5$ bits/value mean savings opportunity (often neglected). Especially for such continuous distributions, there is also discussed quantization approach through optimized continuous \emph{quantization density function} $q$, which inverse CDF (cumulative distribution function) $Q$ on regular 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 of increased entropy due to more uniform distribution. Optimizing both turns out leading to nearly uniform quantization here, with automatized tail handling.
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