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
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Fast texture synthesis using tree-structured vector quantization
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
Texture Synthesis by Non-Parametric Sampling
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Fragment-based image completion
ACM SIGGRAPH 2003 Papers
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
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Texture optimization for example-based synthesis
ACM SIGGRAPH 2005 Papers
Image completion with structure propagation
ACM SIGGRAPH 2005 Papers
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
Algorithms for simultaneous sparse approximation: part II: Convex relaxation
Signal Processing - Sparse approximations in signal and image processing
Image Completion Using Global Optimization
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Constrained and SNR-Based Solutions for TV-Hilbert Space Image Denoising
Journal of Mathematical Imaging and Vision
Inpainting and Zooming Using Sparse Representations
The Computer Journal
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
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
Texture Synthesis with Grouplets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Mathematical Imaging and Vision
Disocclusion: a variational approach using level lines
IEEE Transactions on Image Processing
Simultaneous structure and texture image inpainting
IEEE Transactions on Image Processing
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
Region filling and object removal by exemplar-based image inpainting
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
Selective extraction of entangled textures via adaptive PDE transform
Journal of Biomedical Imaging - Special issue on Mathematical Methods for Images and Surfaces 2011
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This article presents a new adaptive framework for locally parallel texture modeling. Oscillating patterns are modeled with functionals that constrain the local Fourier decomposition of the texture. We first introduce a texture functional which is a weighted Hilbert norm. The weights on the local Fourier atoms are optimized to match the local orientation and frequency of the texture. This adaptive model is used to solve image processing inverse problems, such as image decomposition and inpainting. The local orientation and frequency of the texture component are adaptively estimated during the minimization process. To improve inpainting performances over large missing regions, we introduce a highly nonconvex generalization of our texture model. This new model constrains the amplitude of the texture and allows one to impose an arbitrary oscillation profile. Numerical results illustrate the effectiveness of the method.