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
Dimension reduction by local principal component analysis
Neural Computation
Atomic Decomposition by Basis Pursuit
SIAM Review
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional
International Journal of Computer Vision
Removing camera shake from a single photograph
ACM SIGGRAPH 2006 Papers
Total variation minimizing blind deconvolution with shock filter reference
Image and Vision Computing
Image Super-Resolution by TV-Regularization and Bregman Iteration
Journal of Scientific Computing
Model-Guided Adaptive Recovery of Compressive Sensing
DCC '09 Proceedings of the 2009 Data Compression Conference
PCA-based spatially adaptive denoising of CFA images for single-sensor digital cameras
IEEE Transactions on Image Processing
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Adaptive total variation denoising based on difference curvature
Image and Vision Computing
A plurality of sparse representations is better than the sparsest one alone
IEEE Transactions on Information Theory
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image super-resolution via sparse representation
IEEE Transactions on Image Processing
Super-resolution with sparse mixing estimators
IEEE Transactions on Image Processing
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
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Sparse representation based modeling has been successfully used in many image-related inverse problems such as deblurring, super-resolution and compressive sensing. The heart of sparse representations lies on how to find a space (spanned by a dictionary of atoms) where the local image patch exhibits high sparsity and how to determine the image local sparsity. To identify the locally varying sparsity, it is necessary to locally adapt the dictionary learning process and the sparsity-regularization parameters. However, spatial adaptation alone runs into the risk of over-fitting the data because variation and invariance are two sides of the same coin. In this work, we propose two sets of complementary ideas for regularizing image reconstruction process: (1) the sparsity regularization parameters are locally estimated for each coefficient and updated along with adaptive learning of PCA-based dictionaries; (2) a nonlocal self-similarity constraint is introduced into the overall cost functional to improve the robustness of the model. An efficient alternative minimization algorithm is present to solve the proposed objective function and then an effective image reconstruction algorithm is presented. The experimental results on image deblurring, super-resolution and compressive sensing demonstrate that the proposed image reconstruct method outperforms many existing image reconstruction methods in both PSNR and visual quality assessment.