It is more than 30 years ago I learned digital logic from Blakeslee's Digital Design with MSI and LSI. These days I program an Arduino. I have my hands full just reinventing the spokes of a 20 year old wheel.
I think you have a fascinating problem. Suppose you treat your computer program as a black box where you feed pages of data into one end and you get pages of output data out the other end. Suppose you say each page of data is an x,y grid of image values. You could say, your problem is for a central pixel in the image, you want to write a truth table. An initial truth table is the values and locations of the pixels from the immediate preceding image that when always present always result in the specific value of that pixel.
Your image processing process probably uses data from several preceding images to come up with the result. If it takes five preceding images, then the truth table for a single pixel picks up five more blocks of data about the state of the surrounding pixels. No matter how wonderful the computer program may seem to be, it is still a finite state engine. The present state of the image or output (we hypothesize) should be dependent on the some number of previous states of the image.
The process is a classic series dance steps for extracting the essential predecessor logic states. The Blakeslee book models this better than I can remember after all these years. The steps are normalize, simplify, flag all the dont't care states and gracefully conceal or wrap the data to handle the physical edges . When you have one of these cubic things, you go through a simplification process. first, you normalize the input data which means remove the numerical clutter and have a single number. Another feature of the extraction process is you sort the truth table output column and input columns and you try to mark as many of the input columns with does-not-matter as possible. A third thing is, you set a limit on the depth of the input data and that means the possible values for an output point are limited because the permuted possibilities are capped, and that cap is usually an exponent like 2^N.
The resulting gadget will be a truth table that grinds out something like x=1 for a=1, b=0, c=1, d=0 and on and on.
Unlike rewriting the software and putting it on a programmable gate array, This is an approach at writing a state table that produces an approximate pixel based on looking at a chunk of images containing that pixel.