Nonlinear total variation based noise removal algorithms
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Markov random field modeling in computer vision
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Iterative methods for total variation denoising
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A unified approach to statistical tomography using coordinate descent optimization
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A new efficient approach for the removal of impulse noise from highly corrupted images
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Deterministic edge-preserving regularization in computed imaging
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Fast, robust total variation-based reconstruction of noisy, blurred images
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Markovian reconstruction using a GNC approach
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IEEE Transactions on Image Processing
Weighted median image sharpeners for the World Wide Web
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Selective removal of impulse noise based on homogeneity level information
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Nonlinear image recovery with half-quadratic regularization
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Permutation weighted order statistic filter lattices
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Splines in Higher Order TV Regularization
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Image Deblurring in the Presence of Impulsive Noise
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A comparison of three total variation based texture extraction models
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Fast Global Minimization of the Active Contour/Snake Model
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Minimization of a Detail-Preserving Regularization Functional for Impulse Noise Removal
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A new method for parameter estimation of edge-preserving regularization in image restoration
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An Improved LOT Model for Image Restoration
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Journal of Mathematical Imaging and Vision
Mumford-Shah regularizer with contextual feedback
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An Adaptive Method for Recovering Image from Mixed Noisy Data
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Fast Two-Phase Image Deblurring Under Impulse Noise
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An efficient median filter based method for removing random-valued impulse noise
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New total variation regularized L1 model for image restoration
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Adaptive Variational Method for Restoring Color Images with High Density Impulse Noise
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An efficient two-phase L1-TV method for restoring blurred images with impulse noise
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An Augmented Lagrangian Method for TVg+L1-norm Minimization
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Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction
IEEE Transactions on Image Processing
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SIAM Journal on Scientific Computing
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Document image analysis: issues, comparison of methods and remaining problems
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International Journal of Computer Vision
Rainbow of computer science
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Domain decomposition methods with graph cuts algorithms for total variation minimization
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Structure-Texture decomposition by a TV-Gabor model
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ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part IV
A fast and exact algorithm for total variation minimization
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Fuzzy based diffusion coefficient function in anisotropic diffusion for impulse noise removal
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Toward designing intelligent PDEs for computer vision: An optimal control approach
Image and Vision Computing
Proximity algorithms for the L1/TV image denoising model
Advances in Computational Mathematics
A restoration algorithm for images contaminated by mixed Gaussian plus random-valued impulse noise
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Dictionary learning based impulse noise removal via L1-L1 minimization
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Exact Histogram Specification for Digital Images Using a Variational Approach
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International Journal of Computer Vision
A fixed-point augmented Lagrangian method for total variation minimization problems
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Total variation regularization algorithms for images corrupted with different noise models: a review
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Hybrid regularization image deblurring in the presence of impulsive noise
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A Combined First and Second Order Variational Approach for Image Reconstruction
Journal of Mathematical Imaging and Vision
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We consider signal and image restoration using convex cost-functions composed of a non-smooth data-fidelity term and a smooth regularization term. We provide a convergent method to minimize such cost-functions. In order to restore data corrupted with outliers and impulsive noise, we focus on cost-functions composed of an ℓ1 data-fidelity term and an edge-preserving regularization term. The analysis of the minimizers of these cost-functions provides a natural justification of the method. It is shown that, because of the ℓ1 data-fidelity, these minimizers involve an implicit detection of outliers. Uncorrupted (regular) data entries are fitted exactly while outliers are replaced by estimates determined by the regularization term, independently of the exact value of the outliers. The resultant method is accurate and stable, as demonstrated by the experiments. A crucial advantage over alternative filtering methods is the possibility to convey adequate priors about the restored signals and images, such as the presence of edges. Our variational method furnishes a new framework for the processing of data corrupted with outliers and different kinds of impulse noise.