Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
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
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
Globally Optimal Geodesic Active Contours
Journal of Mathematical Imaging and Vision
Second-order Cone Programming Methods for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Error Bounds for Finite-Difference Methods for Rudin-Osher-Fatemi Image Smoothing
SIAM Journal on Numerical Analysis
Exact optimization of discrete constrained total variation minimization problems
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Total variation minimization and a class of binary MRF models
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Error Bounds for Finite-Difference Methods for Rudin-Osher-Fatemi Image Smoothing
SIAM Journal on Numerical Analysis
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In this paper we study finite-difference approximations to the variational problem using the bounded variation (BV) smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an upwind finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by the first author for a simpler, less isotropic, finite-difference approximation to the (isotropic) BV seminorm. We introduce a multiscale method for speeding up the approximation of both Chambolle's original method and of the new formulation of the upwind scheme. We demonstrate numerically that the multiscale method is effective, and we provide numerical examples that illustrate both the qualitative and quantitative behavior of the solutions of the numerical formulations.