Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing

By Abderrahim Elmoataz, Olivier Lezoray, Sébastien Bougleux. IEEE Transactions on Image Processing, 2008

506 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/6ffe1276146c94b8738e581ed7425c76bdbb1810

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

The Little Engine That Could: Regularization by Denoising (RED) (2016, unknown): “R e d i s t r i bu ti on s ub j ec t t o S I A M li ce n s e o r c opy r i gh t; s ee h tt p :// www . s i a m . o r g /j ou r n a l s / o j s a . php surprising comeback of the Laplacian regularization in a much more sophisticated form, as reported in [47, 48, 49, 50, 51, 52, 53, 54, 55, 56].”
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, background): “…γ > 0 , solve the optimization problem The ﬁrst-order optimality conditions of the convex objective function in (16) show that (see, e.g., [4], [29, Section III-A], [40, Proposition 1]) the optimal reconstruction is given by or, equivalently, f = ˆ h ( Ł ) y , where ˆ h ( λ ) := 1 1+ γλ can be…”
Group-Based Sparse Representation for Image Restoration (2014, background): “Due to the utilization of self-similarity prior by adaptive nonlocal graph, nonlocal regularization terms produce superior results over the local ones, with sharper image edges and more image details [33], [36].”
Solving Inverse Problems With Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity (2010, methodology): “The self-similarity patch-based approaches have been equally addressed in the framework of partial differential equations [28], [34], [73].”
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction (2010, methodology): “in [22] also used graph Laplacian in the discrete setting for image denoising.”
Non-local Color Image Denoising with Convolutional Neural Networks (2016, background): “More recently, a different regularization paradigm has been introduced where non-local operators are employed to define new regularization functionals [10, 14, 19, 22, 40].”
Universal Denoising Networks : A Novel CNN Architecture for Image Denoising (2017, background): “(3) can also be used to describe non-local regularization functionals such as those in [10, 14, 20, 25, 44].”
Towards the Augmented Pathologist: Challenges of Explainable-AI in Digital Pathology (2017, unknown): “This approach is based on an interesting nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing (Elmoataz et al., 2008), where graphs are the shared representation.”
Non-local Regularization of Inverse Problems (2008, methodology): “In order to do so, we use a non-local graph inspired by the non-local means filtering [6], which has been used in several recent methods for denoising, see for instance [15,17].”
Image denoising with nonlocal spectral graph wavelets (2010, methodology): “[13] studied regularization on arbitrary graph domains, including image processing applications employing nonlocal graphs, with a variational framework employing the p-Laplacian, a nonlinear (for general p) operator reducing to the graph Laplacian for p = 2.”
Vertex-Frequency Analysis on Graphs (2013, background): “This well-known property has been extensively utilized in a wide range of problems, including spectral clustering [10], machine learning [11, Section III], and ill-posed inverse problems in image processing [12].”