  Image compression with upsampling encodes information to succeedingly
increase image resolution, for example by encoding differences in FUIF and JPEG
XL. It is useful for progressive decoding, also often can improve compression
ratio - both for lossless compression and e.g. DC coefficients of lossy.
However, the currently used solutions rather do not exploit context dependence
for encoding of such upscaling information. This article discusses simple
inexpensive general techniques for this purpose, which allowed to save on
average $0.645$ bits/difference (between $0.138$ and $1.489$) for the last
upscaling for 48 standard $512\times 512$ grayscale 8 bit images - compared to
assumption of fixed Laplace distribution. Using least squares linear regression
of context to predict center of Laplace distribution gave on average $0.393$
bits/difference savings. The remaining savings were obtained by additionally
predicting width of this Laplace distribution, also using just the least
squares linear regression.
  For RGB images, optimization of color transform alone gave mean $\approx
4.6\%$ size reduction comparing to standard YCrCb if using fixed transform,
$\approx 6.3\%$ if optimizing transform individually for each image. Then
further mean $\approx 10\%$ reduction was obtained if predicting Laplace
parameters based on context. The presented simple inexpensive general
methodology can be also used for different types of data like DCT coefficients
in lossy image compression.

Image and Video Processing;Machine Learning;Multimedia;Machine Learning