To add on @MarcusMüller: in image processing, a constant pixel value shift is often not perceived (as a global scaling), leaving aside saturation issues. In video sequences, illumination may change from one frame to the other. This may induce the noise to have a mean (as a scaling). Also, quantization on integers can change the mean. So often the presence of this shift in noise in undecidable, and related images are sometimes corrected to have the same central tendency (128, mean, median) before further processing. Common image analysis tools and measures are shift insensitive (edge detection, textural analysis, SSIM).
if the subsequent analysis should reveal patterns, fluctuations, assuming zero mean (no DC component) is thus common, unless it is important to use a mean as a reference.
More important in image are background disturbances, where the average illumination (slowly ) varies non-uniformly across the image (like shadow effects), as in the following (darker on the bottom)
Here, oner may ask what is the true mean: the dark gray on the bottom, or the light gray on the top (or something else)?