One of my coworkers shared some of his work showing deconstruction/reconstruction of an image using singular value decomposition:
Full album here. He has an online library used to create this effect, which is pretty neat: https://github.com/t-mart/svdimg
He also shared a cool video using Fourier transforms to decompose / reconstruct images.
I don't know enough math to really take advantage of something like this, but I feel like someone who does would be able to take this to the next level and really get some cool, broken/glitchy results.