In this paper, we propose a regularization technique for noisy-image super-resolution and image denoising. Total variation (TV) regularization is adopted in many image processing applications to preserve the local smoothness. However, TV prior is prone to oversmoothness, staircasing effect, and contrast losses. Nonlocal TV (NLTV) mitigates the contrast losses by adaptively weighting the smoothness based on the similarity measure of image patches. Although it suppresses the noise effectively in the flat regions, it might leave residual noise surrounding the edges especially when the image is not oversmoothed. To address this problem, we propose the bilateral spectrum weighted total variation (BSWTV). Specially, we apply a locally adaptive shrink coefficient to the image gradients and employ the eigenvalues of the covariance matrix of the weighted image gradients to effectively refine the weighting map and suppress the residual noise. In conjunction with the data fidelity term derived from a mixed Poisson–Gaussian noise model, the objective function is decomposed and solved by the alternating direction method of multipliers (ADMM) algorithm. In order to remove the outliers and facilitate the convergence stability, the weighting map is smoothed by a Gaussian filter with an iteratively decreased kernel width and updated in a momentum-based manner in each ADMM iteration. We benchmark our method with the state-of-the-art approaches on the public real-world datasets for super-resolution and image denoising. Experiments show that the proposed method obtains outstanding performance for super-resolution and achieves promising results for denoising on real-world images.

中文翻译：

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噪声图像超分辨率和图像去噪的双边频谱加权总变化

在本文中，我们提出了一种用于噪声图像超分辨率和图像去噪的正则化技术。许多图像处理应用程序都采用了总变异 (TV) 正则化来保持局部平滑度。然而，电视先验容易出现过度平滑、阶梯效应和对比度损失。Nonlocal TV (NLTV) 通过基于图像块的相似性度量对平滑度进行自适应加权来减轻对比度损失。虽然它在平坦区域有效地抑制了噪声，但它可能会在边缘周围留下残余噪声，特别是当图像没有过度平滑时。为了解决这个问题，我们提出了双边频谱加权总变异（BSWTV）。特别，我们对图像梯度应用局部自适应收缩系数，并利用加权图像梯度的协方差矩阵的特征值来有效地细化加权图并抑制残留噪声。结合源自混合泊松-高斯噪声模型的数据保真度项，通过乘法器交替方向法 (ADMM) 算法对目标函数进行分解和求解。为了去除异常值并促进收敛稳定性，加权图由具有迭代减小内核宽度的高斯滤波器平滑，并在每次 ADMM 迭代中以基于动量的方式更新。我们在公共现实世界数据集上使用最先进的方法对我们的方法进行基准测试，以进行超分辨率和图像去噪。