An adaptive method for image restoration based on high-order total variation and inverse gradient

Abstract

The total variation (TV) regularization model for image restoration is widely utilized due to its edge preservation properties. Despite its advantages, the TV regularization can obtain spurious oscillations in flat regions of digital images and thus recent works advocate high-order TV regularization models. In this work, we propose an adaptive image restoration method based on a combination of first-order and second-order total variations regularization with an inverse-gradient-based adaptive parameter. The proposed model removes noise effectively and preserves image structures. Due to the adaptive parameter estimation based on the inverse gradient, it avoids the staircasing artifacts associated with TV regularization and its variant models. Experimental results indicate that the proposed method obtains better restorations in terms of visual quality as well as quantitatively. In particular, our proposed adaptive higher-order TV method obtained (19.3159, 0.7172, 0.90985, 0.79934, 0.99838) PSNR, SSIM, MS-SSIM, F-SIM, and P-SIM values compared to related models such as the TV-Bounded Hessian (18.9735, 0.6599, 0.8718, 0.73833, 0.99767), and TV-Laplacian (19.0345, 0.6719, 0.88198, 0.75405, 0.99789).