Perturbation of the Eigenvectors of the Graph Laplacian: Application to Image Denoising

Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain

Inverse imaging problems are inherently under-determined, and hence it is important to employ appropriate image priors for regularization. One recent popular prior---the graph Laplacian regularizer---assumes that the target pixel patch is smooth with respect to an appropriately chosen graph. However, the mechanisms and implications of imposing the graph Laplacian regularizer on the original inverse problem are not well understood. To address this problem, in this paper we interpret neighborhood graphs of pixel patches as discrete counterparts of Riemannian manifolds and perform analysis in the…

Deep Graph Laplacian Regularization for Robust Denoising of Real Images

Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image noise. In this work, we combine the robustness merit of model-based approaches and the learning power of data-driven approaches for real image denoising. Specifically, by integrating graph Laplacian regularization as a trainable module into a deep learning framework, we are less susceptible to overfitting than pure CNN-based approaches, achieving higher robust…

基于Retinex的图像去噪/对比度增强使用梯度图拉普拉斯正则化器

Retinex-based Image Denoising / Contrast Enhancement using Gradient Graph Laplacian Regularizer

针对低光图像噪声问题，提出基于Retinex理论的快速恢复方案，利用GLR和GGLR正则化分别建模反射率和照明分量，通过交替优化与CG求解，实现高效去噪与对比度增强。

具有社区结构的图集合的谱重心

The Spectral Barycentre of a Set of Graphs with Community Structure

针对处理图值数据的重心图构建问题，提出基于归一化图拉普拉斯矩阵特征值的多尺度谱距离，通过特征向量结构约束确保重心继承拓扑，实验验证其在随机块模型及真实图场景的有效性与收敛性。

The exact Laplacian spectrum for the Dyson hierarchical network

We consider the Dyson hierarchical graph $\mathcal{G}$, that is a weighted fully-connected graph, where the pattern of weights is ruled by the parameter $σ\in (1/2, 1]$. Exploiting the deterministic recursivity through which $\mathcal{G}$ is built, we are able to derive explicitly the whole set of the eigenvalues and the eigenvectors for its Laplacian matrix. Given that the Laplacian operator is intrinsically implied in the analysis of dynamic processes (e.g., random walks) occurring on the graph, as well as in the investigation of the dynamical properties of connected structures themselves (e…