Nonlinear regularizations of TV based PDEs for image processing
Andrea Louise Bertozzi, John B. Greer, Stanley Osher, Kevin R. Vixie · Contemporary mathematics - American Mathematical Society · 2005
ABSTRACT. We consider both second order and fourth order TV-based PDEs for image processing in one space dimension. A general class of nonlinear regularizations of the TV functional result in well-posed uniformly parabolic equations in two dimensions. However the fourth order analogue (Osher et. al. Multiscale Methods and Simulation 1(3) 2003) based on a total variation minimization in an H −1 norm, has very different properties. In particular, nonlinear regularizations should have special structure in order to guarantee that the regularized PDE does not produce finite time singularities.