The authors prove the $\Gamma$-convergence of a shearlet-adapted Ginzburg-Landau(-type) functional to a multiple of the $TV$ seminorm. The design of the functional was inspired by the diffuse-interface wavelet Ginzburg-Landau (GL) energy introduced by J.D. in collaboration with A.Bertozzi. The shearlet GL energy provides the isotropy that the wavelet GL lacks. It opens a new perspective on the implementation and utilization of the TV-related methods.
The generalized notions of the direction-adaptive functionals (primarily related to variational image processing) based on the energies of a similar class are considered. The problem of recovering a weighted-TV-like functional corresponding to any given Wulff shape is addressed.