Image Decomposition Using Bregman-GTV and Meyer´s G-Norm

In order to avoid stair casing and preserve small scale texture information for the classical total variation regularization, a new minimization energy functional model for image decomposition is proposed. We firstly introduce a generalized total variational regularization. The oscillatory component containing texture and/or noise is modeled in generalized function space. And then, the proposed model is numerically implemented by using a preconditioned Split Bregman method. Experiments show that the proposed model can avoid efficiently the staircasing effect, at the same time, both well remain edge and texture.