We started with a project where we denoised normals to surfaces, then
fit the surface to the normals, which we regarded as solving a 4th
order PDE via some kind of splitting. This led to remarkably successful
algorithms for L1 tpe minimizations, constrained and unconstrained. These
include L1, TV, B1,1, nonlocal TV,... Bregman iteration, in its various
incarnations popped up and turned out to be unreasonably effective. I'll
discuss this which is joint work with many people.