Spatially dependent regularization parameter selection in total generalized variation models for image restoration

The automated spatially dependent regularization parameter selection framework of [9] for multi-scale image restoration is applied to total generalized variation (TGV) of order two. Well-posedness of the underlying continuous models is discussed and an algorithm for the numerical solution is developed. Experiments confirm that due to the spatially adapted regularization parameter the method allows for a faithful and simultaneous recovery of fine structures and smooth regions in images. Moreover, because of the TGV regularization term, the adverse staircasing effect, which is a well-known drawback of the total variation regularization, is avoided.