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
SIAM Journal on Numerical Analysis
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
SUSAN—A New Approach to Low Level Image Processing
International Journal of Computer Vision
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Markov Random Fields with Efficient Approximations
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Non-Local Algorithm for Image Denoising
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional
International Journal of Computer Vision
Efficient Belief Propagation for Early Vision
International Journal of Computer Vision
Nonlocal Image and Movie Denoising
International Journal of Computer Vision
Adaptive kernel-based image denoising employing semi-parametric regularization
IEEE Transactions on Image Processing
An improved anisotropic diffusion model for detail- and edge-preserving smoothing
Pattern Recognition Letters
On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
Watershed-based maximum-homogeneity filtering
IEEE Transactions on Image Processing
A segmentation-based regularization term for image deconvolution
IEEE Transactions on Image Processing
Image Denoising by Averaging of Piecewise Constant Simulations of Image Partitions
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
Image Denoising in Mixed Poisson–Gaussian Noise
IEEE Transactions on Image Processing
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This paper addresses the problem of image denoising which is still a valid challenge at the crossing of functional analysis and statistics. We herein propose a novel pixel-based algorithm, which formulates the image denoising problem as the maximum a posterior (MAP) estimation problem using Markov random fields (MRFs). Such an MAP estimation problem is equivalent to a maximum likelihood (ML) estimation constrained on spatial homogeneity and is NP-hard in discrete domain. To make it tractable, we convert it to a continuous label assignment problem based on a Gaussian MRF model and then obtain a closed form globally optimal solution. Since the Gaussian MRFs tend to over-smooth images and blur edges, our algorithm incorporates the pre-estimated image edge information into the energy function construction and therefore better preserves the image structures. In the algorithm, patch similarity based pairwise interaction is also involved to better preserve image details and make the algorithm more robust to noise. Based on the theoretical analysis on the deviation caused by the discretization from obtained continuous global optimum to discrete output, we demonstrate the guaranteed optimal property of our algorithm. Both quantitative and qualitative comparative experimental results are given to demonstrate the better performance of our algorithm over several existing state-of-the-art related algorithms.