I assume there are no photos because the actual images on the sensor will look like gibberish - it'll effectively be two different images overlaid, and look a total mess.

However, feed that mess into AI, and it might successfully be able to use it to see both wide and far.

If CAT scan imagery exists, I suppose this sort of image processing shouldn't be impossible to do-- though I readily admit I have no idea what the logic behind it might look like without some sort of wavelength-based filtering that would make a photographer shudder.

Tomographic reconstruction is in principal pretty straightforward (Radon transform). MRI is much (much), fwiw, though RF not optics.

I don't think wavelength filtering will help you here, as you don't control the input at all. Some sort of splitter in the optical chain might, but you'd be halving your imaging photons with all that entails. Or you can have e.g. a telephoto center and a wide fringe. It's an interesting idea.