See https://en.wikipedia.org/wiki/Tikhonov_regularization
https://en.wikipedia.org/wiki/Regularization_by_spectral_fil...
I think (although they're a little handwavey about it) that their "Gaussian blur" prior must be of this form. They certainly talk about it penalising high frequency components.
The total variation method they mention is a generalisation of this too.
When I was younger I took some drawing lessons because I hoped to be an architect, and the first thing we learned was precisely to undo this instinct and see the world as a flat thing -- this is why artists are seen stereotypically as extending their arm and looking at their brush with one eye -- they're using it to measure the distance of points in their visual field as a static field, as contrasted to the dynamic field that can't be put on paper.