Many aspects of CV and signal processing in general produce almost magical results. It's a little less magical when you think back to stats examples of fitting a curve to some signal + (known) noise process. For linear models, the noise term can get really bad before simple regression won't persevere. Least squares in one form or another finds lots of use in image processing.

Images are just functions, and almost all of the mathematical techniques that you would use to analyze one domain hold for the other. Certain perturbations such as camera jitter are easier to deal with as "undoing" them is tantamount to assuming some underlying regularity/structure on the signal and filtering accordingly. Others, such as removing an occlusion, are harder. Humans do it well thanks to our power of inference, learned from the litany of visual examples that we take in over the course of a lifetime. It's not trivial getting an algorithm to visualize what should have been behind the person who photobombed your insta, but we do it somewhat naturally.

For occlusions and finding relationships between partially overlapping scenes, really interesting things are happening with deep learning. For noisy images, techniques continue to improve. Compressed sensing and signal recovery is an active area of research that's already paid huge dividends in many fields, especially medical imaging. I can't wait to see what becomes possible in the next five years. And, as has been noted - this article is dated. There are already more powerful techniques using deep learning for image super resolution and deblurring.