Title: Derivative-free diffuse interface functionals, their anisotropy and variational convergence
Speaker: Julia Dobrosotskaya (Case Western Reserve University MAMS Department)
Abstract: Fourier analysis provides many elegant approaches to differential operators and related tools in PDE-based image processing. Replacing differential operators with the operators based on multiscale sparse representation systems (such as wavelets or composite wavelets, including shearlets), leads to the design of a new class of adaptively anisotropic operators. These operators fit into a variety of applied signal processing settings, in particular, allowing for derivative-free diffuse interface approximations to the anisotropic TV (total variation) functional.