GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Nonlinear Image Filtering with Edge and Corner Enhancement
IEEE Transactions on Pattern Analysis and Machine Intelligence
A nonlinear filter for film restoration and other problems in image processing
CVGIP: Graphical Models and Image Processing
SIAM Journal on Applied Mathematics
On the Incorporation of Time-delay Regularization into Curvature-based Diffusion
Journal of Mathematical Imaging and Vision
Fractional differentiation for edge detection
Signal Processing - Special issue: Fractional signal processing and applications
Stability and local feature enhancement of higher order nonlinear diffusion filtering
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
A Volterra type model for image processing
IEEE Transactions on Image Processing
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Two Enhanced Fourth Order Diffusion Models for Image Denoising
Journal of Mathematical Imaging and Vision
Image Sharpening via Sobolev Gradient Flows
SIAM Journal on Imaging Sciences
Gradient-based Wiener filter for image denoising
Computers and Electrical Engineering
On a System of Adaptive Coupled PDEs for Image Restoration
Journal of Mathematical Imaging and Vision
A coupled variational model for image denoising using a duality strategy and split Bregman
Multidimensional Systems and Signal Processing
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Two new nonlocal nonlinear diffusion models for noise reduction are proposed, analyzed and implemented. They are both a close relative of the celebrated Perona-Malik equation. In a way, they can be viewed as a new regularization paradigm for Perona-Malik. They do preserve and enhance the most cherished features of Perona-Malik while delivering well-posed equations which admit a stable natural discretization. Unlike other regularizations, however, certain piecewise smooth functions are (meta)stable equilibria and, as a consequence, their dynamical behavior and that of their discrete implementations can be fully understood and do not lead to any "paradox". The presence of nontrivial equilibria also explains why blurring is kept in check. One of the models has been proved to be well-posed. Numerical experiments are presented that illustrate the main features of the new models and that provide insight into their interesting dynamical behavior as well as demonstrate their effectiveness as a denoising tool.