I disagree, your suggestion of deconvolution in stacks of perceptrons in layers of neural networks, and Fast Fourier transform is like rolling up an Abrams tank to a tea party.

I suggest you read Chapter 2, specifically section 2.3 of "Computer Vision, a modern approach" by Forsyth and ponce. There they define the precise optical mechanisms of radiosity, exitance, interreflection, spectrosity, Specularities, illumination, and untangling all that between pinhole in the camera and the object in the image using photometric stereo (two eyes) and motion of a single camera.

We need to untangle what kind of glass specularities we're dealing with and exactly how the bird shit that interfered with the photons between source and target.