On the Relation between Anisotropic Diffusion and Iterated Adaptive Filtering
Proceedings of the 30th DAGM symposium on Pattern Recognition
Homogeneity similarity based image denoising
Pattern Recognition
Two Enhanced Fourth Order Diffusion Models for Image Denoising
Journal of Mathematical Imaging and Vision
Frequency domain regularization of d-dimensional structure tensor-based directional fields
Image and Vision Computing
Multigrid method for fractional diffusion equations
Journal of Computational Physics
Image Sharpening via Sobolev Gradient Flows
SIAM Journal on Imaging Sciences
Adaptive Fractional-order Multi-scale Method for Image Denoising
Journal of Mathematical Imaging and Vision
Fully fractional anisotropic diffusion for image denoising
Mathematical and Computer Modelling: An International Journal
A circulant preconditioner for fractional diffusion equations
Journal of Computational Physics
International Journal of Sensor Networks
Preconditioned iterative methods for fractional diffusion equation
Journal of Computational Physics
A coupled variational model for image denoising using a duality strategy and split Bregman
Multidimensional Systems and Signal Processing
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This paper introduces a new class of fractional-order anisotropic diffusion equations for noise removal. These equations are Euler-Lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function, so the proposed equations can be seen as generalizations of second-order and fourth-order anisotropic diffusion equations. We use the discrete Fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain. It is one important aspect of the algorithm that it considers the input image as a periodic image. To overcome this problem, we use a folded algorithm by extending the image symmetrically about its borders. Finally, we list various numerical results on denoising real images. Experiments show that the proposed fractional-order anisotropic diffusion equations yield good visual effects and better signal-to-noise ratio.