You should look up image sensor dark noise. One way to reduce dark noise is taking an exposure without any light on the sensor, it should give you the fixed pattern which can be subtracted from your scene image. Dark noise is sensitive to temperature and exposure time, so you should try to do this under similar conditions.
I implemented it just now. Turns out when performing the subtraction on the raw data before applying the color space conversion LUT, it's also necessary to add the mean of the noise image's pixel values because otherwise some bias is lost and the entire image's brightness changes. With this in place, it seems to work. Interestingly enough, this even results in noticeable noise reduction when the noise image was not recorded in the same environment but only with the same camera settings!
When performing the subtraction after applying the LUT (that is, result = apply_lut(raw) - apply_lut(raw_noise) instead of result = apply_lut(raw - raw_noise + mean(raw_noise))), the result is quite different for reasons that I don't fully understand yet, but the noise is reduced in the same way. This will need some further investigation.
