  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) $\rho\sim \exp(-(|x-\mu|/\sigma)^{\kappa})$ family, leading to
maximum likelihood estimated (MLE) $\kappa\approx 0.5$ instead of Laplace
distribution $\kappa=1$ - 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 $\mu, \sigma, \kappa$
parameters) for DCT coefficients from already decoded coefficients in the
current and neighboring DCT blocks. Predicting values $(\mu)$ from neighboring
blocks 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 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.
