We review work with Guy Gilboa on the use of nonlocal operators to define new types of functionals for image processing and elsewhere. This gives an advantage in handling textures and repetitive structures. then we will discuss new joint work with Hayden Schaeffer, Russle Caflisch and Cory Hauck on sparse solvers for multiscale PDE. we seem to automatically very efficiently represent the dynamics of multiscale PDE's including Navier-Stokes equation, with a very simple sparsification idea.