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
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
SIAM Journal on Numerical Analysis
SUSAN—A New Approach to Low Level Image Processing
International Journal of Computer Vision
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Digital Picture Processing
A mathematical theory of communication
ACM SIGMOBILE Mobile Computing and Communications Review
Texture Synthesis by Non-Parametric Sampling
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Context-based surface completion
ACM SIGGRAPH 2004 Papers
Unsupervised, Information-Theoretic, Adaptive Image Filtering for Image Restoration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Smoothing by Example: Mesh Denoising by Averaging with Similarity-Based Weights
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Neighborhood filters and PDE’s
Numerische Mathematik
Space-Time Adaptation for Patch-Based Image Sequence Restoration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlocal Image and Movie Denoising
International Journal of Computer Vision
3D wavelet subbands mixing for image denoising
Journal of Biomedical Imaging
Self-similarity of Images in the Fourier Domain, with Applications to MRI
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
Examining the Role of Scale in the Context of the Non-Local-Means Filter
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
A Simple, General Model for the Affine Self-similarity of Images
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
A non-local regularization strategy for image deconvolution
Pattern Recognition Letters
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
Gaussian KD-trees for fast high-dimensional filtering
ACM SIGGRAPH 2009 papers
Journal of Mathematical Imaging and Vision
Nonlocal Variational Image Deblurring Models in the Presence of Gaussian or Impulse Noise
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A Variational Framework for Non-local Image Inpainting
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Image sequence denoising via sparse and redundant representations
IEEE Transactions on Image Processing
Generalizing the Nonlocal-means to super-resolution reconstruction
IEEE Transactions on Image Processing
Self-similarity driven color demosaicking
IEEE Transactions on Image Processing
Topology Preserving Linear Filtering Applied to Medical Imaging
SIAM Journal on Imaging Sciences
Iterated nonlocal means for texture restoration
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Non-local means variants for denoising of diffusion-weighted and diffusion tensor MRI
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention
Fast non local means denoising for 3d MR images
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Universal discrete denoising: known channel
IEEE Transactions on Information Theory
De-noising by soft-thresholding
IEEE Transactions on Information Theory
The staircasing effect in neighborhood filters and its solution
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
Sparse Representation for Color Image Restoration
IEEE Transactions on Image Processing
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
IEEE Transactions on Image Processing
Solving the inverse problem of image zooming using "self-examples"
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
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The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding performance when the image model corresponds to the algorithm assumptions but fail in general and create artifacts or remove fine structures in images. The main focus of this paper is, first, to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms and, second, to propose a nonlocal means (NL-means) algorithm addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the “method noise,” defined as the difference between a digital image and its denoised version. The NL-means algorithm is proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods is compared in four ways; mathematical: asymptotic order of magnitude of the method noise under regularity assumptions; perceptual-mathematical: the algorithms artifacts and their explanation as a violation of the image model; quantitative experimental: by tables of $L^2$ distances of the denoised version to the original image. The fourth and perhaps most powerful evaluation method is, however, the visualization of the method noise on natural images. The more this method noise looks like a real white noise, the better the method.