How linear combinations of pixels used in PAQ8px bmp models were chosen?

Is there any theory or experiments that justify choice of linear combinations of pixel neighborhood used in PAQ8px image models?

Currently, I am trying to implement part of im8bit model of PAQ8px in hardware (FPGA) for grayscale image compression. I am curios to understand, how these combinations were selected. Is it worth to run any tests, to look for any better sets of these linear combinations or not? Maybe I can use less number of these combinations and achieve similar results, thus saving hardware resources of FPGA. There is a lot to think about.

Hey, here is an explanation on the subject. Of course, Marcio Pais can also give you details if you want something very specific.
https://www.mdpi.com/2076-3417/9/13/2681 In the PDF, the explanations start at around page 5.

Depending on which image types you are trying to compress, you can give up on a lot of models. Do you have a benchmark or target you are trying to achieve?

> I am curios to understand, how these combinations were selected.

Logistic mixing makes sure that adding any predictions with any new context
won't significantly hurt the overall result (so any new context normally improves it).
Then we can use common sense - any adjacent pixels or pixel combinations
can be used as context, but contexts with higher entropy would gather
statistics slower, so won't improve compression if same context is not repeated frequently.
AFAIK, in paq8 case, developers just add simple contexts one by one based on common sense
or imagination, then tweak weights manually to improve compression, or discard
the ideas that didn't work.

> Is it worth to run any tests, to look for any better sets of these linear combinations or not?

Very much yes.
You can just take the modelling framework from paq8 - counters, mixers, APM, basic models.
Even that is not perfect, but its easier than starting from nothing.
Also there're some explanations here: http://mattmahoney.net/dc/dce.html#Section_43

And then you can automate the process described above -
gather some relevant image samples, design a quality metric
(for example, it can be a linear mix of compressed size, compression time and used memory),
then add contexts with optimized pixel weights to improve the metric.

Just with that, its very likely to beat results of any paq model eventually,
mostly because paq developers consider automated parameter optimization
to be "impure" or something.

Although of course, for some specific image types (eg. book scans)
it may be better to build specific transformations (eg. OCR)
or submodels (eg. match model) before applying plain context mixing.