Remove an image through subtraction? Firstly, I'm no video professional, I'm an audio professional. Video theory is a dark area for me. So I will use an audio-type analogy in this question.

In audio editing, it is possible to subtract one waveshape from a bunch of other waves by inverting the phase of the wave(phase subtraction). While this is a simple, easy to understand process, due to my lack of knowledge of digital video processing, I am unsure if this process is an available tool in video editing. My logical mind tells me that it is. I know in nature, like in bubbles, phase interactions cause interesting effects.

I need to use this process on a video to remove the axis scales from a 3D spectrogram, so that everything else in the video except the axis scales are left.

For this I assume I need an isolated image of the thing I want to subtract i.e. the axis scales. I'm using Adobe Premiere Pro or After Effects, whichever is best for this. The Image I want to remove is stationary in the video.

Any advice on how to do this in Adobe AE/PP if it can be done is appreciated.
It is possible and works in a similar manner. What's different is that normal pixel values in video are always positive, whereas it's normal for audio to go both positive and negative several thousand times per second.

If you have a copy of the axes without the spectrum, you can overlay the image with the spectrum on top of the image of the axes and set the blend mode of the spectrum image to "difference." That will subtract the image of the axes from the spectrum image and leave black where the axes were.

If you don't want black, but some other color, you can use an image mask that sets the axes to an alpha value of 0 and the rest of the image to an alpha value of 1 (or 255 if you're working in 8 bit per channel mode). Then put some other color underneath the masked footage.

EDIT: I forgot to mention that the image of the axes alone should be black wherever you want the original image to come through. (Because you're then subtracting 0 from the original image in those areas.)