Integrating the advantages of two recently developed total generalized variation (TGV) and Gabor wavelets, this letter presents a new weighted TGV-Gabor model for the challenging problem of cartoon-texture image decomposition. Computationally, by introducing two dual variables, we formulate a highly efficient numerical method based on the primal-dual framework in detail. At last, in comparison with several existing advanced variational models, experimental simulations clearly illustrate the outstanding performance of our proposed edge-preserving model, especially in separating the larger structural features from the smaller textural details completely and maintaining the sharp edges and weak contours simultaneously.

Total generalised variation (TGV) methods are highly efficient for eliminating the staircase artefacts. However, with the aim of further avoiding over‐smoothing edges, this study investigates a new weighted second‐order TGV scheme for image restoration. Computationally, an alternating split Bregman algorithm is employed to obtain the optimal solution recursively. Moreover, the rigorous convergence analysis of the resulting algorithm is also described in brief. In comparison with the results of current state‐of‐the‐art regulariser techniques, numerical simulations distinctly demonstrate the competitive performance of the proposed strategy in feature preservation and staircasing effect suppression.