LAUSR

In this paper, we propose a new artifact-free variational model for JPEG/JPEG 2000 decompression based on a cartoon-texture decomposition scheme. The new infimal convolution-type regularization associated with total generalized variation (TGV) and shearlet transform can reconstruct piecewise smooth images with structured textures well due to the property of shearlet of representing the positions and orientations of singularities, which can be interpreted as the oscillation texture parts. In order to enhance the qualities of reconstructed images, we incorporate an $L^{2}$ cost functional into the model, then the discretization of such functional can be easily solved by the generic proximal primal–dual method. Numerical experiments show that our proposed model is competitive with the learning method—trainable nonlinear reaction diffusion—in terms of texture preservation, and outperforms the TV-based and TGV-based variational methods.