Nonlocal Adaptive Biharmonic Regularizer for Image Restoration
Nonlocal Adaptive Biharmonic Regularizer for Image Restoration
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DOI：
10.1007/s10851-022-01129-4
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发表时间：
2022-11
影响因子：
2
通讯作者：
Ying Wen;L. Vese;Kehan Shi;Zhichang Guo;Jiebao Sun
中科院分区：
文献类型：
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作者：
Ying Wen;L. Vese;Kehan Shi;Zhichang Guo;Jiebao Sun
本文结合四阶模型(保斜率)和非局部方法(保纹理)的优点，提出了一种用于图像恢复的非局部自适应双调和正则化方法。在图像去模糊和去噪的基础上，将所提出的非局部自适应双调和正则化方法应用于图像修复，并提出了一种权矩阵归一化方法，弥补了非局部权值矩阵信息丢失的不足，加快了修复过程。证明了解的存在唯一性。讨论了均值不变性等数学性质。对于数值解，我们使用了梯度下降和有限差分方法来设计显式和半隐式格式。在合成图像、真实图像和纹理图像上给出了图像恢复的数值结果。与局部四阶模型、非局部二阶模型以及其他最新方法进行了比较，说明了该模型的优越性。
In this paper, we propose a nonlocal adaptive biharmonic regularization term for image restoration, combining the advantages of fourth-order models (preserving slopes) and nonlocal methods (preserving textures). Besides the image deblurring and denoising, we apply the proposed nonlocal adaptive biharmonic regularizer to image inpainting, and a weight matrix normalization method is developed to cover the shortage of information loss of the nonlocal weight matrix and accelerate the inpainting process. The existence and uniqueness of the solution are proved. The mathematical property such as mean invariance is discussed. For the numerical solution, we employ thegradient descent and finite difference methods to design explicit and semi-implicit schemes. Numerical results for image restoration are shown on synthetic images, real images, and texture images. Comparisons with local fourth-order models, nonlocal second-order models, and other state-of-the-art methods are made, which help to illustrate the advantages of the proposed model.