SIAM Journal on Control and Optimization
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
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Removing camera shake from a single photograph
ACM SIGGRAPH 2006 Papers
Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
High-quality motion deblurring from a single image
ACM SIGGRAPH 2008 papers
Non-local Regularization of Inverse Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Variational denoising of partly textured images
Journal of Visual Communication and Image Representation
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
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
SIAM Journal on Optimization
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Image Recovery via Nonlocal Operators
Journal of Scientific Computing
IEEE Transactions on Image Processing
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
Total variation blind deconvolution
IEEE Transactions on Image Processing
Variational denoising of partly textured images by spatially varying constraints
IEEE Transactions on Image Processing
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
IEEE Transactions on Image Processing
Hierarchical representation of discrete data on graphs
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Image deblurring with matrix regression and gradient evolution
Pattern Recognition
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Nonlinear Multilayered Representation of Graph-Signals
Journal of Mathematical Imaging and Vision
Robust visual tracking with discriminative sparse learning
Pattern Recognition
Journal of Computational and Applied Mathematics
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Non-blind motion deblurring problems are highly ill-posed and so it is quite difficult to find the original sharp and clean image. To handle ill-posedness of the motion deblurring problem, we use nonlocal total variation (abbreviated as TV) regularization approaches. Nonlocal TV can restore periodic textures and local geometric information better than local TV. But, since nonlocal TV requires weighted difference between pixels in the whole image, it demands much more computational resources than local TV. By using the linearization of the fidelity term and the proximal function, our proposed algorithm does not require any inversion of blurring operator and nonlocal operator. Therefore, the proposed algorithm is very efficient for motion deblurring problems. We compare the numerical performance of our proposed algorithm with that of several state-of-the-art algorithms for deblurring problems. Our numerical results show that the proposed method is faster and more robust than state-of-the-art algorithms on motion deblurring problems.