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
Removing Noise and Preserving Details with Relaxed Median Filters
Journal of Mathematical Imaging and Vision
Relations Between Regularization and Diffusion Filtering
Journal of Mathematical Imaging and Vision
SIAM Journal on Scientific Computing
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Coherence-Enhancing Diffusion Filtering
International Journal of Computer Vision
Geometric surface smoothing via anisotropic diffusion of normals
Proceedings of the conference on Visualization '02
A Review of Nonlinear Diffusion Filtering
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Image Sharpening by Flows Based on Triple Well Potentials
Journal of Mathematical Imaging and Vision
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's
International Journal of Computer Vision
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image restoration combining a total variational filter and a fourth-order filter
Journal of Visual Communication and Image Representation
An Improved Hybrid Model for Molecular Image Denoising
Journal of Mathematical Imaging and Vision
A Self-governing Hybrid Model for Noise Removal
PSIVT '09 Proceedings of the 3rd Pacific Rim Symposium on Advances in Image and Video Technology
An Anisotropic Fourth-Order Partial Differential Equation for Noise Removal
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A TV-stokes denoising algorithm
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Stability and local feature enhancement of higher order nonlinear diffusion filtering
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Behavioral analysis of anisotropic diffusion in image processing
IEEE Transactions on Image Processing
Adaptive smoothing respecting feature directions
IEEE Transactions on Image Processing
Optimally isotropic Laplacian operator
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
Fourth-order variational model with local-constraints for denoising images with textures
International Journal of Computational Vision and Robotics
Shock coupled fourth-order diffusion for image enhancement
Computers and Electrical Engineering
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Fourth-order nonlinear diffusion filters used for image noise removal are mainly isotropic filters. It means that the spatially varying diffusivity determined by a diffusion function is applied on the image regardless of the orientation of its local features. However, the optimal choice of parameters in the numerical solver of these filters for having a minimal distortion of the image features results in forming speckle noise on the denoised image and a very slow convergence rate especially when the noise level is moderately high. In this paper, a new fourth-order nonlinear diffusion filter is introduced, which has an anisotropic behavior on the image features. In the proposed filter, it is shown that a suitable choice for a set of diffusivity functions to unevenly control the strength of the diffusion on the directions of the level set and gradient leads to a good edge preservation capability compared to the other diffusion or regularization filters. The comparison of the results obtained by the proposed filter with those of the other second and fourth-order filters shows that the proposed method produces a noticeable improvement in the quality of denoised images evaluated subjectively and quantitatively.