on Statistical data analysis based on the L1-norm and related methods
on Statistical data analysis based on the L1-norm and related methods
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Convex analysis and variational problems
Convex analysis and variational problems
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Selection of Optimal Stopping Time for Nonlinear Diffusion Filtering
International Journal of Computer Vision
Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing
Journal of Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
Dual Norms and Image Decomposition Models
International Journal of Computer Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
Efficient Beltrami flow using a short time kernel
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Estimation of the optimal variational parameter via SNR analysis
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Structure-Texture decomposition by a TV-Gabor model
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
An adaptive level set method for nondifferentiable constrained image recovery
IEEE Transactions on Image Processing
Image restoration subject to a total variation constraint
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
Estimation of optimal PDE-based denoising in the SNR sense
IEEE Transactions on Image Processing
Variational denoising of partly textured images by spatially varying constraints
IEEE Transactions on Image Processing
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
Projected Gradient Based Color Image Decomposition
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Locally Parallel Textures Modeling with Adapted Hilbert Spaces
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Decorrelating the structure and texture components of a variational decomposition model
IEEE Transactions on Image Processing
Journal of Mathematical Imaging and Vision
Fast cartoon + texture image filters
IEEE Transactions on Image Processing
Locally Parallel Texture Modeling
SIAM Journal on Imaging Sciences
A Nonlocal Version of the Osher-Solé-Vese Model
Journal of Mathematical Imaging and Vision
Geometrical and textural component separation with adaptive scale selection
MUSCLE'11 Proceedings of the 2011 international conference on Computational Intelligence for Multimedia Understanding
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We examine the general regularization model which is based on total-variation for the structural part and a Hilbert-space norm for the oscillatory part. This framework generalizes the Rudin-Osher-Fatemi and the Osher-Sole-Vese models and opens way for new denoising or decomposition methods with tunable norms, which are adapted to the nature of the noise or textures of the image. We give sufficient conditions and prove the convergence of an iterative numerical implementation, following Chambolle's projection algorithm.In this paper we focus on the denoising problem. In order to provide an automatic solution, a systematic method for choosing the weight between the energies is imperative. The classical method for selecting the weight parameter according to the noise variance is reformulated in a Hilbert space sense. Moreover, we generalize a recent study of Gilboa-Sochen-Zeevi where the weight parameter is selected such that the denoised result is close to optimal, in the SNR sense. A broader definition of SNR, which is frequency weighted, is formulated in the context of inner products. A necessary condition for maximal SNR is provided. Lower and upper bounds on the SNR performance of the classical and optimal strategies are established, under quite general assumptions.