A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
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
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Image decomposition application to SAR images
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
IEEE Transactions on Image Processing
Minimizing the total variation under a general convex constraint for image restoration
IEEE Transactions on Image Processing
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
Constrained and SNR-Based Solutions for TV-Hilbert Space Image Denoising
Journal of Mathematical Imaging and Vision
A comparison of three total variation based texture extraction models
Journal of Visual Communication and Image Representation
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Noisy Image Decomposition: A New Structure, Texture and Noise Model Based on Local Adaptivity
Journal of Mathematical Imaging and Vision
Image decomposition combining staircase reduction and texture extraction
Journal of Visual Communication and Image Representation
Extracting Grain Boundaries and Macroscopic Deformations from Images on Atomic Scale
Journal of Scientific Computing
ICISP '08 Proceedings of the 3rd international conference on Image and Signal Processing
(Φ,Φ*) Image Decomposition Models and Minimization Algorithms
Journal of Mathematical Imaging and Vision
Image Decomposition Based on Curvelet and Wave Atom
ISICA '08 Proceedings of the 3rd International Symposium on Advances in Computation and Intelligence
Detection of Retinal Blood Vessels Based on Nonlinear Projections
Journal of Signal Processing Systems
Projected Gradient Based Color Image Decomposition
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Pose Invariant Shape Prior Segmentation Using Continuous Cuts and Gradient Descent on Lie Groups
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
On a Decomposition Model for Optical Flow
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Weighted and extended total variation for image restoration and decomposition
Pattern Recognition
Uniform and textured regions separation in natural images towards MPM adaptive denoising
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Identification of grain boundary contours at atomic scale
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
On the total variation dictionary model
IEEE Transactions on Image Processing
Nonstandard diffusion in image restoration and decomposition
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Journal of Mathematical Imaging and Vision
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
Journal of Scientific Computing
Fast cartoon + texture image filters
IEEE Transactions on Image Processing
An Augmented Lagrangian Method for TVg+L1-norm Minimization
Journal of Mathematical Imaging and Vision
Segmenting and indexing old documents using a letter extraction
GREC'09 Proceedings of the 8th international conference on Graphics recognition: achievements, challenges, and evolution
IEEE Transactions on Image Processing
Review article: Edge and line oriented contour detection: State of the art
Image and Vision Computing
A novel variational model for image segmentation
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Proximal Algorithms for Multicomponent Image Recovery Problems
Journal of Mathematical Imaging and Vision
A primal-dual gradient method for image decomposition based on (BV, H-1)
Multidimensional Systems and Signal Processing
Locally Parallel Texture Modeling
SIAM Journal on Imaging Sciences
An adaptive variational model for image decomposition
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Constrained total variation minimization and application in computerized tomography
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
A study of non-smooth convex flow decomposition
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Structure-Texture decomposition by a TV-Gabor model
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Combined geometric-texture image classification
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Adaptive Fractional-order Multi-scale Method for Image Denoising
Journal of Mathematical Imaging and Vision
A Nonlocal Version of the Osher-Solé-Vese Model
Journal of Mathematical Imaging and Vision
Denoising 3d medical images using a second order variational model and wavelet shrinkage
ICIAR'12 Proceedings of the 9th international conference on Image Analysis and Recognition - Volume Part II
Uzawa block relaxation methods for color image restoration
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume 2
Nonlinear Multilayered Representation of Graph-Signals
Journal of Mathematical Imaging and Vision
Ancient documents denoising and decomposition using aujol and chambolle algorithm
GREC'11 Proceedings of the 9th international conference on Graphics Recognition: new trends and challenges
Hi-index | 0.00 |
Following a recent work by Y. Meyer, decomposition models into a geometrical component and a textured component have recently been proposed in image processing. In such approaches, negative Sobolev norms have seemed to be useful to modelize oscillating patterns. In this paper, we compare the properties of various norms that are dual of Sobolev or Besov norms. We then propose a decomposition model which splits an image into three components: a first one containing the structure of the image, a second one the texture of the image, and a third one the noise. Our decomposition model relies on the use of three different semi-norms: the total variation for the geometrical component, a negative Sobolev norm for the texture, and a negative Besov norm for the noise. We illustrate our study with numerical examples.