Gradient-domain image decomposition for image recovery

This paper aims to introduce a convex prior based on gradient-domain image decomposition (GID) for image recovery. As a useful class of convex priors, total variation (TV) and its variants have been widely investigated. Among them, total generalized variation (TGV) is paid much attention recently, because it provides rich visual quality around edges and gradation regions in recovered images. This paper gives a general perspective: the TGV can be regarded as a GID and thus can be extended to more general formulation. Specifically, by introducing some priors promoting desired properties on gradient components which cannot be treated efficiently by the TGV, the restored image would attain better visual quality. As a practical instance, we incorporate block nuclear norm (BNN), which can characterize local low rankness, into the GID framework to keep the visual quality of well-patterned textures. Consequently, the GID provides better subjective visual quality and less reconstruction error in missing pixel recovery, than the TGV-based and the TV/BNN-based regularization methods.