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
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Convergence Rates in Forward--Backward Splitting
SIAM Journal on Optimization
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Dual Norms and Image Decomposition Models
International Journal of Computer Vision
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
Noisy Image Decomposition: A New Structure, Texture and Noise Model Based on Local Adaptivity
Journal of Mathematical Imaging and Vision
Fractional Variational Model and Algorithm for Image Denoising
ICNC '08 Proceedings of the 2008 Fourth International Conference on Natural Computation - Volume 05
Multiplicative Noise Removal with Spatially Varying Regularization Parameters
SIAM Journal on Imaging Sciences
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Variational denoising of partly textured images by spatially varying constraints
IEEE Transactions on Image Processing
Fractional-Order Anisotropic Diffusion for Image Denoising
IEEE Transactions on Image Processing
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The total variation model proposed by Rudin, Osher, and Fatemi performs very well for removing noise while preserving edges. However, it favors a piecewise constant solution in BV space which often leads to the staircase effect, and small details such as textures are often filtered out with noise in the process of denoising. In this paper, we propose a fractional-order multi-scale variational model which can better preserve the textural information and eliminate the staircase effect. This is accomplished by replacing the first-order derivative with the fractional-order derivative in the regularization term, and substituting a kind of multi-scale norm in negative Sobolev space for the L 2 norm in the fidelity term of the ROF model. To improve the results, we propose an adaptive parameter selection method for the proposed model by using the local variance measures and the wavelet based estimation of the singularity. Using the operator splitting technique, we develop a simple alternating projection algorithm to solve the new model. Numerical results show that our method can not only remove noise and eliminate the staircase effect efficiently in the non-textured region, but also preserve the small details such as textures well in the textured region. It is for this reason that our adaptive method can improve the result both visually and in terms of the peak signal to noise ratio efficiently.