From what I can tell skimming their papers, no. Their technique really is based on solving a PDE to fill in the gaps in the image. Neat idea and I'm a little

From what I can tell skimming their papers, no. Their technique really is based on solving a PDE to fill in the gaps in the image. Neat idea and I'm a little surprised that it works so well. Compressed sensing relies on an equivalence between a discrete and a continuous optimization problem under very specific assumptions, which allows the sparsest possible solution to an underdetermined linear system to be found. In this work, there's no optimization, so no compressed sensing.