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
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Multigrid Method for Ill-Conditioned Symmetric Toeplitz Systems
SIAM Journal on Scientific Computing
Rate of Convergence of Some Space Decomposition Methods for Linear and Nonlinear Problems
SIAM Journal on Numerical Analysis
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
An energy-minimizing interpolation for robust multigrid methods
SIAM Journal on Scientific Computing
Multigrid
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
SIAM Journal on Scientific Computing
An Algebraic Multigrid Approach for Image Analysis
SIAM Journal on Scientific Computing
Global and uniform convergence of subspace correction methods for some convex optimization problems
Mathematics of Computation
MULTIGRID ONE SHOT METHODS FOR OPTIMAL CONTROL PROBLEMS: INFINITE DIMENSIONAL CONTROL
MULTIGRID ONE SHOT METHODS FOR OPTIMAL CONTROL PROBLEMS: INFINITE DIMENSIONAL CONTROL
Acceleration Methods for Total Variation-Based Image Denoising
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
A computational algorithm for minimizing total variation in image restoration
IEEE Transactions on Image Processing
Multigrid anisotropic diffusion
IEEE Transactions on Image Processing
Fast, robust total variation-based reconstruction of noisy, blurred images
IEEE Transactions on Image Processing
Minimizing the total variation under a general convex constraint for image restoration
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization
IEEE Transactions on Image Processing
Multilevel algorithm for a Poisson noise removal model with total-variation regularization
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Convex Hodge Decomposition and Regularization of Image Flows
Journal of Mathematical Imaging and Vision
A fast optimization transfer algorithm for image inpainting in wavelet domains
IEEE Transactions on Image Processing
Updating preconditioners for nonlinear deblurring and denoising image restoration
Applied Numerical Mathematics
Stopping Criteria for Anisotropic PDEs in Image Processing
Journal of Scientific Computing
A Multilevel Algorithm for Simultaneously Denoising and Deblurring Images
SIAM Journal on Scientific Computing
A robust multigrid approach for variational image registration models
Journal of Computational and Applied Mathematics
Domain decomposition methods with graph cuts algorithms for total variation minimization
Advances in Computational Mathematics
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Image restoration has been an active research topic and variational formulations are particularly effective in high quality recovery. Although there exist many modelling and theoretical results, available iterative solvers are not yet robust in solving such modeling equations. Recent attempts on developing optimisation multigrid methods have been based on first order conditions. Different from this idea, this paper proposes to use piecewise linear function spanned subspace correction to design a multilevel method for directly solving the total variation minimisation. Our method appears to be more robust than the primal-dual method (Chan et al., SIAM J. Sci. Comput. 20(6), 1964---1977, 1999) previously found reliable. Supporting numerical results are presented.