In this paper, a new relaxed second-order total generalized variational model is proposed for image denoising. In this model, the regularization term is a combination of a gradient operator and weighted divergence operator, while the data fidelity terms we used is l2-norm. The weighted divergence operator in the regularization is used to adjust the higher-order smoothing term, which can reduce the computational complexity and guarantee the discrete accuracy. Moreover, the Augmented Lagrangian algorithm, which produced several closed form solutions is used to solve the proposed RTGV method. Then we applied the denoising model to both gray and color image denoising, and performed numerous experiments. Our algorithm is discussed from several aspects, including influence of parameters, numerical discretization and comparisons with other methods. Numerical experimental results demonstrate that this technique has the significant advantage in preserving image features and can effectively prevent the staircase artifacts when compared to several other classical existing based methods.

Mengge Cheng, Huayan Zhang. A New Relaxed Total Generalized Variation (RTGV) Technique for Image Denoising. Academic Journal of Computing & Information Science (2022), Vol. 5, Issue 14: 1-10. https://doi.org/10.25236/AJCIS.2022.051401.

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