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
Numerical Methods for p-Harmonic Flows and Applications to Image Processing
SIAM Journal on Numerical Analysis
Second-order Cone Programming Methods for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Journal of 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)
Filling-in by joint interpolation of vector fields and gray levels
IEEE Transactions on Image Processing
Noise removal using smoothed normals and surface fitting
IEEE Transactions on Image Processing
An Improved LOT Model for Image Restoration
Journal of Mathematical Imaging and Vision
A Dual Formulation of the TV-Stokes Algorithm for Image Denoising
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Anisotropic Smoothing Using Double Orientations
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Image Denoising Using TV-Stokes Equation with an Orientation-Matching Minimization
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Total-Variation Based Piecewise Affine Regularization
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A two-step model for image denoising using a duality strategy and surface fitting
Journal of Computational and Applied Mathematics
Orientation-Matching Minimization for Image Denoising and Inpainting
International Journal of Computer Vision
An Anisotropic Fourth-Order Diffusion Filter for Image Noise Removal
International Journal of Computer Vision
A Modified TV-Stokes Model for Image Processing
SIAM Journal on Scientific Computing
Augmented Lagrangian Method for Generalized TV-Stokes Model
Journal of Scientific Computing
A New TV-Stokes Model with Augmented Lagrangian Method for Image Denoising and Deconvolution
Journal of Scientific Computing
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In this paper, we propose a two-step algorithm for denoising digital images with additive noise. Observing that the isophote directions of an image correspond to an incompressible velocity field, we impose the constraint of zero divergence on the tangential field. Combined with an energy minimization problem corresponding to the smoothing of tangential vectors, this constraint gives rise to a nonlinear Stokes equation where the nonlinearity is in the viscosity function. Once the isophote directions are found, an image is reconstructed that fits those directions by solving another nonlinear partial differential equation. In both steps, we use finite difference schemes to solve. We present several numerical examples to show the effectiveness of our approach.