SUSAN—A New Approach to Low Level Image Processing
International Journal of Computer Vision
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
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
Nonlocal Image and Movie Denoising
International Journal of Computer Vision
A non-local regularization strategy for image deconvolution
Pattern Recognition Letters
Gaussian KD-trees for fast high-dimensional filtering
ACM SIGGRAPH 2009 papers
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
Image Recovery via Nonlocal Operators
Journal of Scientific Computing
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
Stabilization of Flicker-Like Effects in Image Sequences through Local Contrast Correction
SIAM Journal on Imaging Sciences
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
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
Solving the inverse problem of image zooming using "self-examples"
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
Adaptive discrete Laplace operator
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part II
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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 image fine structures. 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 describe the nonlocal means (NL-means) algorithm introduced in 2005 and its more recent extensions. The mathematical analysis is based on the analysis of the "method noise," defined as the difference between a digital image and its denoised version. NL-means, which uses image self-similarities, is proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods are 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; perceptual-mathematical, analysis of algorithms when applied to noise samples; quantitative experimental, by tables of L2 distances of the denoised version to the original image.