Local mesh refinement multilevel techniques
SIAM Journal on Scientific and Statistical Computing
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
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
Robust multigrid methods for nonsmooth coefficient elliptic linear systems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Multigrid
Uniform convergence of the multigrid V-cycle for an anisotropic problem
Mathematics of Computation
Applied Numerical Mathematics
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
SIAM Journal on Scientific Computing
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image Restoration
SIAM Journal on Numerical Analysis
Numerical Methods for p-Harmonic Flows and Applications to Image Processing
SIAM Journal on Numerical Analysis
Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion
Journal of Scientific Computing
On Effective Methods for Implicit Piecewise Smooth Surface Recovery
SIAM Journal on Scientific Computing
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Multigrid solution techniques for anisotropic structured linear systems
Applied Numerical Mathematics
On high-order denoising models and fast algorithms for vector-valued images
IEEE Transactions on Image Processing
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Noise removal using smoothed normals and surface fitting
IEEE Transactions on Image Processing
Inpainting of Binary Images Using the Cahn–Hilliard Equation
IEEE Transactions on Image Processing
Multigrid Geometric Active Contour Models
IEEE Transactions on Image Processing
Curvature regularity for multi-label problems - standard and customized linear programming
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Homotopy method for a mean curvature-based denoising model
Applied Numerical Mathematics
Nonlinear multigrid method for solving the anisotropic image denoising models
Numerical Algorithms
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Image denoising has been a research topic deeply investigated within the last two decades. Excellent results have been obtained by using such models as the total variation (TV) minimization by Rudin, Osher, and Fatemi [Phys. D, 60 (1992), pp. 259-268], which involves solving a second order PDE. In more recent years some effort has been made [Y.-L. You and M. Kaveh, IEEE Trans. Image Process., 9 (2000), pp. 1723-1730; M. Lysaker, S. Osher, and X.-C. Tai, IEEE Trans. Image Process., 13 (2004), pp. 1345-1357; M. Lysaker, A. Lundervold, and X.-C. Tai, IEEE Trans. Image Process., 12 (2003), pp. 1579-1590; Y. Chen, S. Levine, and M. Rao, SIAM J. Appl. Math., 66 (2006), pp. 1383-1406] in improving these results by using higher order models, particularly to avoid the staircase effect inherent to the solution of the TV model. However, the construction of stable numerical schemes for the resulting PDEs arising from the minimization of such high order models has proved to be very difficult due to high nonlinearity and stiffness. In this paper, we study a curvature-based energy minimizing model [W. Zhu and T. F. Chan, Image Denoising Using Mean Curvature, preprint, http://www.math.nyu.edu/ wzhu/], for which one has to solve a fourth order PDE. For this model we develop two new algorithms: a stabilized fixed point method and, based upon this, an efficient nonlinear multigrid (MG) algorithm. We will show numerical experiments to demonstrate the very good performance of our MG algorithm.