Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Inverse Scale Space Theory for Inverse Problems
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
Journal of Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Dual Norms and Image Decomposition Models
International Journal of Computer Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
Point-based multiscale surface representation
ACM Transactions on Graphics (TOG)
A tutorial on spectral clustering
Statistics and Computing
Non-local Regularization of Inverse Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
A Variational Framework for Non-local Image Inpainting
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Discrete regularization on weighted graphs for image and mesh filtering
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Partial differences as tools for filtering data on graphs
Pattern Recognition Letters
Nonlocal multiscale hierarchical decomposition on graphs
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
Regularization on discrete spaces
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Total variation minimization and a class of binary MRF models
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
IEEE Transactions on Image Processing
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
IEEE Transactions on Image Processing
Total Variation Projection With First Order Schemes
IEEE Transactions on Image Processing
| Hi-index | 0.00 |
We propose a nonlinear multiscale decomposition of signals defined on the vertex set of a general weighted graph. This decomposition is inspired by the hierarchical multiscale (BV,L 2) decomposition of Tadmor, Nezzar, and Vese (Multiscale Model. Simul. 2(4):554---579, 2004). We find the decomposition by iterative regularization using a graph variant of the classical total variation regularization (Rudin et al, Physica D 60(1---4):259---268, 1992). Using tools from convex analysis, and in particular Moreau's identity, we carry out the mathematical study of the proposed method, proving the convergence of the representation and providing an energy decomposition result. The choice of the sequence of scales is also addressed. Our study shows that the initial scale can be related to a discrete version of Meyer's norm (Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, 2001) which we introduce in the present paper. We propose to use the recent primal-dual algorithm of Chambolle and Pock (J. Math. Imaging Vis. 40:120---145, 2011) in order to compute both the minimizer of the graph total variation and the corresponding dual norm. By applying the graph model to digital images, we investigate the use of nonlocal methods to the multiscale decomposition task. Since the only assumption needed to apply our method is that the input data is living on a graph, we are also able to tackle the task of adaptive multiscale decomposition of irregularly sampled data sets within the same framework. We provide in particular examples of 3-D irregular meshes and point clouds decompositions.