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
Handbook of Image and Video Processing
Handbook of Image and Video Processing
Digital Image Processing
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
Second-order Cone Programming Methods for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional
International Journal of Computer Vision
Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration
SIAM Journal on Scientific Computing
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
Total Variation Models for Variable Lighting Face Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints
SIAM Journal on Numerical Analysis
Simultaneously inpainting in image and transformed domains
Numerische Mathematik
A Fast $\ell$1-TV Algorithm for Image Restoration
SIAM Journal on Scientific Computing
An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise
SIAM Journal on Scientific Computing
An Efficient Primal-Dual Method for $L^1$TV Image Restoration
SIAM Journal on Imaging Sciences
A duality based approach for realtime TV-L1 optical flow
Proceedings of the 29th DAGM conference on Pattern recognition
SIAM Journal on Scientific Computing
Improved Total Variation-Type Regularization Using Higher Order Edge Detectors
SIAM Journal on Imaging Sciences
A property of the minimum vectors of a regularizing functionaldefined by means of the absolute norm
IEEE Transactions on Signal Processing
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
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This paper introduces a proximity operator framework for studying the L1/TV image denoising model which minimizes the sum of a data fidelity term measured in the 驴1-norm and the total-variation regularization term. Both terms in the model are non-differentiable. This causes algorithmic difficulties for its numerical treatment. To overcome the difficulties, we formulate the total-variation as a composition of a convex function (the 驴1-norm or the 驴2-norm) and the first order difference operator, and then express the solution of the model in terms of the proximity operator of the composition. By developing a "chain rule" for the proximity operator of the composition, we identify the solution as fixed point of a nonlinear mapping expressed in terms of the proximity operator of the 驴1-norm or the 驴2-norm, each of which is explicitly given. This formulation naturally leads to fixed-point algorithms for the numerical treatment of the model. We propose an alternative model by replacing the non-differentiable convex function in the formulation of the total variation with its differentiable Moreau envelope and develop corresponding fixed-point algorithms for solving the new model. When partial information of the underlying image is available, we modify the model by adding an indicator function to the minimization functional and derive its corresponding fixed-point algorithms. Numerical experiments are conducted to test the approximation accuracy and computational efficiency of the proposed algorithms. Also, we provide a comparison of our approach to two state-of-the-art algorithms available in the literature. Numerical results confirm that our algorithms perform favorably, in terms of PSNR-values and CPU-time, in comparison to the two algorithms.