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The Total Generalized Variation (TGV) model proves effective in removing texture and background patterns in natural images while suppressing the staircase effect introduced by traditional Total Variation (TV) regularization. Nevertheless, TGV falls short in preserving structural features due to its lack of consideration for such structural features. This paper introduces Overlapping Group Sparsity (OGS) regularization into the TGV model with the specific aim of enhancing denoising, particularly in textured images. By leveraging prior knowledge of sparse structures discernible from first-order and second-order gradients, this model surpasses the conventional TGV models in achieving superior denoising and staircase effect elimination. The model proposed employs a fast split Bregman iteration method to address the L1 regularization problem within the complex TGV model combined with OGS. The experimental results comparing various state-of-the-art denoising TV- and TGV-based models highlight a significant improvement in the denoising performance of the proposed model. Specifically, in comparison to the average values of peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) obtained from other state-of-the-art models, the proposed model demonstrated improvements of 3.5% in PSNR and 3.4% in SSIM.

Denoising on Textured Image using Total Generalized Variation with Overlapping Group Sparsity based on Fast Split Bregman Method