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).

中文翻译：

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一种基于高阶全变分和逆梯度的自适应图像恢复方法

用于图像恢复的总变异 (TV) 正则化模型由于其边缘保留特性而被广泛使用。尽管有优点，电视正则化可以在数字图像的平坦区域获得虚假振荡，因此最近的工作提倡高阶电视正则化模型。在这项工作中，我们提出了一种基于一阶和二阶总变化正则化与基于逆梯度的自适应参数相结合的自适应图像恢复方法。所提出的模型有效地去除了噪声并保留了图像结构。由于基于逆梯度的自适应参数估计，它避免了与 TV 正则化及其变体模型相关的阶梯伪影。实验结果表明，所提出的方法在视觉质量和定量方面都获得了更好的恢复。特别是，我们提出的自适应高阶 TV 方法获得 (19.3159, 0.7172, 0.90985, 0.79934, 0.99838) PSNR、SSIM、MS-SSIM、F-SIM 和 P-SIM 值与相关模型（如 TV-Bounded Hessian (18.9735, 0.6599, 0.8718, 0.73833, 0.99767) 和 TV-Laplacian (19.0345, 0.6719, 0.88198, 0.75405, 0.9978)。