论文标题
改善DCT系数的分布和灵活量化
Improving distribution and flexible quantization for DCT coefficients
论文作者
论文摘要
虽然众所周知，与傅立叶相关转换的AC系数（如JPEG图像压缩的DCT-II）来自拉普拉斯的分布，但经过测试了更一般的EPD（指数功率分布）$ρ\ sim \ sim \ exp \ exp（ - （| x--μ|/σ）^κ）$ hission $ nife nife nibe yive nibe nife lap nife lap inter lap inter lap inter lap nife（mle）$κ$κ- $κ= 1 $ - 这样的替代品可提供$ \ \ \ bits/value的平均节省（每个像素的灰度，RGB最高$ 3 \ times $）。 还讨论了预测来自电流和邻近DCT块中已经解码系数的DCT系数的DCT系数的分布（为$μ，σ，κ$参数）。从相邻块中预测值$（μ）$可以减少阻塞工件，也可以提高压缩率 - 仅预测不确定性/宽度$σ$的预测提供了更大的$ \ $ \ bits/value Bits/value均值储蓄机会（通常被忽略）。 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 （不均匀）量化 - 具有不同尺寸$ n $的量子，并具有速率控制控制。仅优化$ Q $单独的失真会导致显着改善，但是，由于分布更均匀，熵的成本增加。通过自动化的尾部处理，优化两种情况都导致了几乎均匀的量化。
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.
