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
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Variational Image Restoration and Decomposition with Curvelet Shrinkage
Journal of Mathematical Imaging and Vision
Spatial adaptive Bayesian wavelet threshold exploiting scale and space consistency
Multidimensional Systems and Signal Processing
Staircase effect alleviation by coupling gradient fidelity term
Image and Vision Computing
An Improved LOT Model for Image Restoration
Journal of Mathematical Imaging and Vision
Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Two new nonlinear nonlocal diffusions for noise reduction
Journal of Mathematical Imaging and Vision
Properties of Higher Order Nonlinear Diffusion Filtering
Journal of Mathematical Imaging and Vision
Linearized Bregman Iterations for Frame-Based Image Deblurring
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction
IEEE Transactions on Image Processing
SIAM Journal on Imaging Sciences
Orientation-Matching Minimization for Image Denoising and Inpainting
International Journal of Computer Vision
Analysis and Generalizations of the Linearized Bregman Method
SIAM Journal on Imaging Sciences
A Modified TV-Stokes Model for Image Processing
SIAM Journal on Scientific Computing
Multidimensional Systems and Signal Processing
De-noising by soft-thresholding
IEEE Transactions on Information Theory
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
Fractional-Order Anisotropic Diffusion for Image Denoising
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Total Variation Projection With First Order Schemes
IEEE Transactions on Image Processing
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To reduce the staircase effect, high-order diffusion equations are used with high computational cost. Recently, a two-step method with two energy functions has been introduced to alleviate the staircase effect successfully. In the two-step method, firstly, the normal vector of noisy image is smoothed, and then the image is reconstructed from the smoothed normal field. In this paper, we propose a new image restoration model with only one energy function. When the alternating direction method is used, the estimation of the vector field and the reconstruction of the image are interlaced, which makes the new vector field can utilize sufficiently the information of the restored image, thus the constructed vector field is more accurate than that generated by the two-step method. To speed up the computation, the dual approach and split Bregman are employed in our numerical algorithm. The experimental results show that the new model is more effective to filter out the Gaussian noise than the state-of-the-art models.