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
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
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
Dictionary learning algorithms for sparse representation
Neural Computation
Texture Synthesis by Non-Parametric Sampling
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
Journal of Scientific Computing
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
Neural Computation
Learning Overcomplete Representations
Neural Computation
Wire Structure Pattern Extraction and Tracking From X-Ray Images of Composite Mechanisms
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Method of optimal directions for frame design
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 05
International Journal of Computer Vision
Inpainting and Zooming Using Sparse Representations
The Computer Journal
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Journal of Mathematical Imaging and Vision
Texture Synthesis with Grouplets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Online Learning for Matrix Factorization and Sparse Coding
The Journal of Machine Learning Research
Multichannel nonnegative matrix factorization in convolutive mixtures for audio source separation
IEEE Transactions on Audio, Speech, and Language Processing
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
An axiomatic approach to image interpolation
IEEE Transactions on Image Processing
Filling-in by joint interpolation of vector fields and gray levels
IEEE Transactions on Image Processing
Disocclusion: a variational approach using level lines
IEEE Transactions on Image Processing
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
Region filling and object removal by exemplar-based image inpainting
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Sparsity and Morphological Diversity in Blind Source Separation
IEEE Transactions on Image Processing
Morphological Component Analysis: An Adaptive Thresholding Strategy
IEEE Transactions on Image Processing
Sparse Representation for Color Image Restoration
IEEE Transactions on Image Processing
Image decomposition via learning the morphological diversity
Pattern Recognition Letters
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This article proposes a new method for image separation into a linear combination of morphological components. Sparsity in fixed dictionaries is used to extract the cartoon and oscillating content of the image. Complicated texture patterns are extracted by learning adapted local dictionaries that sparsify patches in the image. These fixed and learned sparsity priors define a nonconvex energy, and the separation is obtained as a stationary point of this energy. This variational optimization is extended to solve more general inverse problems such as inpainting. A new adaptive morphological component analysis algorithm is derived to find a stationary point of the energy. Using adapted dictionaries learned from data allows one to circumvent some difficulties faced by fixed dictionaries. Numerical results demonstrate that this adaptivity is indeed crucial in capturing complex texture patterns.