Atomic Decomposition by Basis Pursuit
SIAM Review
Dictionary learning algorithms for sparse representation
Neural Computation
Learning Overcomplete Representations
Neural Computation
A Predual Proximal Point Algorithm Solving a Non Negative Basis Pursuit Denoising Model
International Journal of Computer Vision
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
Sparse and Redundant Modeling of Image Content Using an Image-Signature-Dictionary
SIAM Journal on Imaging Sciences
Online Learning for Matrix Factorization and Sparse Coding
The Journal of Machine Learning Research
Bayesian orthogonal component analysis for sparse representation
IEEE Transactions on Signal Processing
Nonlinear inverse scale space methods for image restoration
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
An affine scaling methodology for best basis selection
IEEE Transactions on Signal Processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Why Simple Shrinkage Is Still Relevant for Redundant Representations?
IEEE Transactions on Information Theory
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Iterative Regularization and Nonlinear Inverse Scale Space Applied to Wavelet-Based Denoising
IEEE Transactions on Image Processing
Sparse Representation for Color Image Restoration
IEEE Transactions on Image Processing
An augmented Lagrangian approach to general dictionary learning for image denoising
Journal of Visual Communication and Image Representation
Dictionary learning based impulse noise removal via L1-L1 minimization
Signal Processing
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Dictionary learning has been a hot topic fascinating many researchers in recent years. Most of existing methods have a common character that the sequences of learned dictionaries are simpler and simpler regularly by minimizing some cost function. This paper presents a novel predual dictionary learning (PDL) algorithm that updates dictionary via a simple gradient descent method after each inner minimization step of Predual Proximal Point Algorithm (PPPA), which was recently presented by Malgouyres and Zeng (2009) [F. Malgouyres, T. Zeng, A predual proximal point algorithm solving a non negative basis pursuit denoising model, Int. J. Comput. Vision 83 (3) (2009) 294-311]. We prove that the dictionary update strategy of the proposed method is different from the current ones because the learned dictionaries become more and more complex regularly. The experimental results on both synthetic data and real images consistently demonstrate that the proposed approach can efficiently remove the noise while maintaining high image quality and presents advantages over the classical dictionary learning algorithms MOD and K-SVD.