Total generalized variation restoration with non-quadratic fidelity

Total variation (TV) based Models have been widely used in image restoration problems. However, these models are always accompanied by staircase effect due to the property of bounded variation (BV) space. In this paper, we present two high order variational models based on total generalized variation (TGV) with two common and important non-quadratic fidelity data terms for blurred images corrupted by impulsive and Poisson noises. Since the direct extension of alternative direction method of multipliers (ADMM) to solve three-block convex minimization problems is not necessarily convergent, we develop an efficient algorithm called Prediction–Correction ADMM to solve our models and also show the convergence of the proposed method. Moreover, we extend our models to deal with color images restoration. Numerical experiments demonstrate that the proposed high order models can reduce staircase effect while preserving edges and outperform classical TV based models in SNR and SSIM values.

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