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A review of image denoising algorithms, with a new one,”Multiscale Modeling and Simulation (2006)

by A Buades, B Coll, J M Morel
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Image denoising by sparse 3D transform-domain collaborative filtering

by Kostadin Dabov, Alessandro Foi, Vladimir Katkovnik, Karen Egiazarian - IEEE TRANS. IMAGE PROCESS , 2007
"... We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2-D image fragments (e.g., blocks) into 3-D data arrays which we call “groups.” Collaborative filtering is a special procedure d ..."
Abstract - Cited by 424 (32 self) - Add to MetaCart
We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2-D image fragments (e.g., blocks) into 3-D data arrays which we call “groups.” Collaborative filtering is a special procedure developed to deal with these 3-D groups. We realize it using the three successive steps: 3-D transformation of a group, shrinkage of the transform spectrum, and inverse 3-D transformation. The result is a 3-D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.

Sparse representation for color image restoration

by Julien Mairal, Julien Mairal, Michael Elad, Michael Elad, Guillermo Sapiro, Guillermo Sapiro - the IEEE Trans. on Image Processing , 2007
"... Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted ..."
Abstract - Cited by 219 (30 self) - Add to MetaCart
Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted dictionaries for images has been a major challenge. The K-SVD has been recently proposed for this task [1], and shown to perform very well for various gray-scale image processing tasks. In this paper we address the problem of learning dictionaries for color images and extend the K-SVD-based gray-scale image denoising algorithm that appears in [2]. This work puts forward ways for handling non-homogeneous noise and missing information, paving the way to state-of-the-art results in applications such as color image denoising, demosaicing, and inpainting, as demonstrated in this paper. EDICS Category: COL-COLR (Color processing) I.
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...versal denoiser of images, which learns the posterior from the given image in a way inspired by the Lempel-Ziv universal compression algorithm. Another path of such works is the Non-Local-Means [38], =-=[39]-=- and related works [40], [41]. Interestingly, the work in [2] belongs to this family as well, as the dictionary can be based on the noisy image itself. Most of the above methods deploy processing of s...

Sparse Representation For Computer Vision and Pattern Recognition

by John Wright, Yi Ma, Julien Mairal, Guillermo Sapiro, Thomas Huang, Shuicheng Yan , 2009
"... Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on non-traditional applications where the goal is not just to obtain a compact high-fidelity representation of the observed signal, but also to extract semantic information. The choice of ..."
Abstract - Cited by 146 (9 self) - Add to MetaCart
Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on non-traditional applications where the goal is not just to obtain a compact high-fidelity representation of the observed signal, but also to extract semantic information. The choice of dictionary plays a key role in bridging this gap: unconventional dictionaries consisting of, or learned from, the training samples themselves provide the key to obtaining state-of-theart results and to attaching semantic meaning to sparse signal representations. Understanding the good performance of such unconventional dictionaries in turn demands new algorithmic and analytical techniques. This review paper highlights a few representative examples of how the interaction between sparse signal representation and computer vision can enrich both fields, and raises a number of open questions for further study.
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...se), with a sparsity of about 1/10th of the signal dimension m. State-of-the-art results obtained in [51] are “shared” with those in [19], which extends the non-local means approach developed in [5], =-=[12]-=-. Interestingly, the two frameworks are quite related, since they both use patches as building blocks (in [51], the sparse coding is applied to all overlapping image patches), and while a dictionary i...

Super-Resolution from a Single Image

by Daniel Glasner, Shai Bagon, Michal Irani
"... Methods for super-resolution can be broadly classified into two families of methods: (i) The classical multi-image super-resolution (combining images obtained at subpixel misalignments), and (ii) Example-Based super-resolution (learning correspondence between low and high resolution image patches fr ..."
Abstract - Cited by 139 (5 self) - Add to MetaCart
Methods for super-resolution can be broadly classified into two families of methods: (i) The classical multi-image super-resolution (combining images obtained at subpixel misalignments), and (ii) Example-Based super-resolution (learning correspondence between low and high resolution image patches from a database). In this paper we propose a unified framework for combining these two families of methods. We further show how this combined approach can be applied to obtain super resolution from as little as a single image (with no database or prior examples). Our approach is based on the observation that patches in a natural image tend to redundantly recur many times inside the image, both within the same scale, as well as across different scales. Recurrence of patches within the same image scale (at subpixel misalignments) gives rise to the classical super-resolution, whereas recurrence of patches across different scales of the same image gives rise to example-based super-resolution. Our approach attempts to recover at each pixel its best possible resolution increase based on its patch redundancy within and across scales. 1.
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...hese two different approaches to SR can be combined in a single unified computational framework. Patch repetitions within an image were previously exploited for noise-cleaning using ‘Non-Local Means’ =-=[4]-=-, as well as a regularization prior for inverse problems [15]. A related SR approach was proposed by [16] for obtaining higher-resolution video frames, by applying the classical SR constraints to simi...

Fields of Experts

by Stefan Roth, Michael J. Black - INTERNATIONAL JOURNAL OF COMPUTER VISION , 2008
"... We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach provides a practical method for learning high-order Markov random field (MRF) models with potential functions that ex ..."
Abstract - Cited by 130 (12 self) - Add to MetaCart
We develop a framework for learning generic, expressive image priors that capture the statistics of natural scenes and can be used for a variety of machine vision tasks. The approach provides a practical method for learning high-order Markov random field (MRF) models with potential functions that extend over large pixel neighborhoods. These clique potentials are modeled using the Product-of-Experts framework that uses nonlinear functions of many linear filter responses. In contrast to previous MRF approaches all parameters, including the linear filters themselves, are learned from training data. We demonstrate the capabilities of this Field-of-Experts model with two example applications, image denoising and image inpainting, which are implemented using a simple, approximate inference scheme. While the model is trained on a generic image database and is not tuned toward a specific application, we obtain results that compete with specialized techniques.

Learning multiscale sparse representations for image and video restoration

by Julien Mairal, Guillermo Sapiro, Michael Elad , 2007
"... Abstract. This paper presents a framework for learning multiscale sparse representations of color images and video with overcomplete dictionaries. A single-scale K-SVD algorithm was introduced in [1], formulating sparse dictionary learning for grayscale image representation as an optimization proble ..."
Abstract - Cited by 103 (21 self) - Add to MetaCart
Abstract. This paper presents a framework for learning multiscale sparse representations of color images and video with overcomplete dictionaries. A single-scale K-SVD algorithm was introduced in [1], formulating sparse dictionary learning for grayscale image representation as an optimization problem, efficiently solved via Orthogonal Matching Pursuit (OMP) and Singular Value Decomposition (SVD). Following this work, we propose a multiscale learned representation, obtained by using an efficient quadtree decomposition of the learned dictionary, and overlapping image patches. The proposed framework provides an alternative to pre-defined dictionaries such as wavelets, and shown to lead to state-of-the-art results in a number of image and video enhancement and restoration applications. This paper describes the proposed framework, and accompanies it by numerous examples demonstrating its strength. Key words. Image and video processing, sparsity, dictionary, multiscale representation, denoising, inpainting, interpolation, learning. AMS subject classifications. 49M27, 62H35
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...ks such as [10, 19, 20, 22, 35, 38]. The proposed algorithm also competes favorably with the most recent and state-of-the-art result in this field [12], which is based on the nonlocal means algorithm =-=[4]-=-. Our framework for color image denoising also competes favorably with the best known algorithm in this field [11], and the results for the other presented applications such as color video denoising a...

Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction

by Xiaoqun Zhang, Martin Burger, Xavier Bresson, Stanley Osher , 2009
"... We propose two algorithms based on Bregman iteration and operator splitting technique for nonlocal TV regularization problems. The convergence of the algorithms is analyzed and applications to deconvolution and sparse reconstruction are presented. ..."
Abstract - Cited by 88 (8 self) - Add to MetaCart
We propose two algorithms based on Bregman iteration and operator splitting technique for nonlocal TV regularization problems. The convergence of the algorithms is analyzed and applications to deconvolution and sparse reconstruction are presented.
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...is is to search for similar image patches in the image and determine the value of the hole using found patches. Texture synthesis also influences the image denoising task. Buades et al. introduced in =-=[2]-=- an efficient denoising model called nonlocal means (NL-means). The model consists in denoising a pixel value by averaging the nearby pixel values with similar structures (patches). Given a reference ...

Generalizing the non-local-means to super-resolution reconstruction

by Matan Protter, Michael Elad, Hiroyuki Takeda, Peyman Milanfar - IN IEEE TRANSACTIONS ON IMAGE PROCESSING , 2009
"... Super-resolution reconstruction proposes a fusion of several low-quality images into one higher quality result with better optical resolution. Classic super-resolution techniques strongly rely on the availability of accurate motion estimation for this fusion task. When the motion is estimated inacc ..."
Abstract - Cited by 81 (4 self) - Add to MetaCart
Super-resolution reconstruction proposes a fusion of several low-quality images into one higher quality result with better optical resolution. Classic super-resolution techniques strongly rely on the availability of accurate motion estimation for this fusion task. When the motion is estimated inaccurately, as often happens for nonglobal motion fields, annoying artifacts appear in the super-resolved outcome. Encouraged by recent developments on the video denoising problem, where state-of-the-art algorithms are formed with no explicit motion estimation, we seek a super-resolution algorithm of similar nature that will allow processing sequences with general motion patterns. In this paper, we base our solution on the Nonlocal-Means (NLM) algorithm. We show how this denoising method is generalized to become a relatively simple super-resolution algorithm with no explicit motion estimation. Results on several test movies show that the proposed method is very successful in providing super-resolution on general sequences.
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...weakest among the recent motion-estimation-free video denoising algorithms, and yet, it is also the simplest. As such, it stands as a good candidate for generalization. The NLM is posed originally in =-=[31]-=- as a single image denoising method, generalizing the well-known bilateral filter [32], [33]. Denoising is obtained by replacing every pixel with a weighted average of its neighborhood. The weights fo...

Nonlocal discrete regularization on weighted graphs: a framework for image and manifold processing

by Abderrahim Elmoataz, Olivier Lezoray, Sébastien Bougleux , 2007
"... We introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing. The approach considers the problem as a variational one, which consists in minimizing a weighted sum of two energy terms: a regularization one that uses a dis ..."
Abstract - Cited by 77 (26 self) - Add to MetaCart
We introduce a nonlocal discrete regularization framework on weighted graphs of the arbitrary topologies for image and manifold processing. The approach considers the problem as a variational one, which consists in minimizing a weighted sum of two energy terms: a regularization one that uses a discrete weighted p-Dirichlet energy, and an approximation one. This is the discrete analogue of recent continuous Euclidean nonlocal regularization functionals. The proposed formulation leads to a family of simple and fast nonlinear processing methods based on the weighted p-Laplace operator, parameterized by the degree p of regularity, the graph structure and the graph weight function. These discrete processing methods provide a graph-based version of recently proposed semi-local or nonlocal processing methods used in image and mesh processing, such as the bilateral filter, the TV digital filter or the nonlocal means filter. It works with equal ease on regular 2D-3D images, manifolds or any data. We illustrate the abilities of the approach by applying it to various types of images, meshes, manifolds and data represented as graphs.
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...lly performed by designing continuous Partial Differential Equations (PDE), whose solutions are discretized in order to fit with the image domain. A complete overview of these methods can be found in =-=[1]-=-, [2], [3], [4] and references therein. In the context of mesh processing, smoothing and denoising are also key processes dedicated to noise removal causing The authors are with the Université de Caen...

Local adaptivity to variable smoothness for exemplar-based image denoising and representation

by Charles Kervrann, Jérôme Boulanger , 2005
"... ..."
Abstract - Cited by 66 (6 self) - Add to MetaCart
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