I bought a cheap medion scanner which turned out to be a bad idea since the light in it is not evenly distributed and gives a kind of vignette How can I correct it in an open source program that runs on linux (I'm thinking gimp or darktable or maybe something else?). My guess would be to do a scan without a negative inside and then somehow add the empty scan as a kind of mask to the scanned image and then tell the program to reverse the colors. I'm using astrodmx for capturing data from the scanner (couldn't find anything better for linux, maybe there's some software that could do the correction at the moment of capturing). Scanner model is medion MD86601.
Assuming that what you get without a negative is a mostly white field with even whiter corners, you can try to use that by adding it as layer in Gimp and setting it to "Divide" mode.
Yuck. Likely faster to get a better scanner.
Try this: Use an image of an 18% grey card. This will give you a non-saturated grey to work with. When you're shooting the greycard, make a range of exposures.
In Gimp take your image, ups the range to 16 bit, divides it by the grey image chosen, then downsamples back to whatever format you choose for archiving.
You may need a smoothing step in there.
You should be able to script this in Gimp.
But you are still losing information. Rescan them.