An augmented Lagrangian method for \(\mathrm{TV}_g +L^1\)-norm minimization

DOI10.1007/s10851-010-0219-1zbMath1255.94019OpenAlexW2241097341MaRDI QIDQ1932808

Jonas Koko, Stéphanie Jehan-Besson

Publication date: 22 January 2013

Published in: Journal of Mathematical Imaging and Vision (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10851-010-0219-1

zbMATH Keywords

total variationgeometric filteringFenchel dualityaugmented Lagrangian\(L^1\)-normUzawa methodsshape retrievalsalt and pepper noise removal

Mathematics Subject Classification ID

Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Inverse problems in optimal control (49N45)

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Cites Work

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• Nonlinear total variation based noise removal algorithms
• Uzawa block relaxation domain decomposition method for the two-body contact problem with Tresca friction
• An integral formula for total gradient variation
• Two-phase approach for deblurring images corrupted by impulse plus Gaussian noise
• Constraints on deformable models: Recovering 3D shape and nonrigid motion
• A geometric model for active contours in image processing
• Geodesic active contours
• An algorithm for total variation minimization and applications
• A variational approach to remove outliers and impulse noise
• Image restoration with discrete constrained total variation. II: Levelable functions, convex priors and non-convex cases
• Image restoration with discrete constrained total variation. I: Fast and exact optimization
• Structure-texture image decomposition -- modeling, algorithms, and parameter selection
• Dual norms and image decomposition models
• Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models
• The TVL1 Model: A Geometric Point of View
• Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
• Digital filters as absolute norm regularizers
• A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
• Noise adaptive soft-switching median filter
• Active contours without edges
• Geometric Level Set Methods in Imaging, Vision, and Graphics
• Space variant median filters for the restoration of impulse noise corrupted images
• Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers
• Aspects of Total Variation RegularizedL¹Function Approximation
• The Total Variation Regularized $L^1$ Model for Multiscale Decomposition
• Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration
• Scale Space and PDE Methods in Computer Vision