Patch reprojections for Non-Local methods

Salmon, Joseph; Strozecki, Yann

doi:10.1016/j.sigpro.2011.08.011

Cited by 48 publications

(27 citation statements)

References 27 publications

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“…At this point, the MLE ( u(x), σ(x)) could be directly computed at each x from the n-tuple (u(y), y ∈ V n x ). In practice, following the idea of [10], we observe better results by using all patches…”

Section: Algorithmmentioning

confidence: 87%

PARIGI: a Patch-based Approach to Remove Impulse-Gaussian Noise from Images

Delon¹,

Desolneux²,

Guillemot³

2016

Image Processing on Line

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In this paper, we present an implementation of the PARIGI method that addresses the problem of the restoration of images affected by impulse noise or by a mixture of Gaussian and impulse noise. The method relies on a patch-based approach, which requires careful choices for both the distance between patches and for the statistical estimator of the original patch. Experiments are performed in the case of pure impulse noise and in the case of a mixture of Gaussian and impulse noise. Source CodeThe source code and the code documentation are available as supplementary material. The documentation is included in the archive. Basic compilation and usage instructions are included in the README.txt file. All those files and the online demo are accessible at the IPOL web page of this article 1 .

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Section: Algorithmmentioning

confidence: 87%

PARIGI: a Patch-based Approach to Remove Impulse-Gaussian Noise from Images

Delon¹,

Desolneux²,

Guillemot³

2016

Image Processing on Line

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“…Those algorithms rely on averaging similar pixels, where the similarity is measured through patches centered on the pixel of interest. Some more elaborate methods have tried to remove artifacts appearing in regions with low redundancy [45] -a phenomenon also known as the rare patch effect [15] -for instance by choosing NLM parameters automatically and locally. A common tool used for this local adaptivity is the Stein Unbiased Risk Estimate (SURE) [15,58,59].…”

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confidence: 99%

Oracle Inequalities and Minimax Rates for Nonlocal Means and Related Adaptive Kernel-Based Methods

Arias-Castro

Salmon²,

Willett³

2012

SIAM J. Imaging Sci.

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Abstract. This paper describes a novel theoretical characterization of the performance of non-local means (NLM) for noise removal. NLM has proven effective in a variety of empirical studies, but little is understood fundamentally about how it performs relative to classical methods based on wavelets or how its parameters should be chosen. For cartoon images and images which may contain thin features and regular textures, the error decay rates of NLM are derived and compared with those of linear filtering, oracle estimators, Yaroslavsky's filter and wavelet thresholding estimators. The trade-off between global and local search for matching patches is examined, and the bias reduction associated with the local polynomial regression version of NLM is analyzed. The theoretical results are validated via simulations for 2D images corrupted by additive white Gaussian noise.Key words. Non-local means (NLM), Yaroslavsky's filter, kernel smoothing, patch-based methods, local polynomial regression, oracle bounds, minimax bounds, cartoon model, textures.1. Introduction. The classical problem of image noise removal has drawn significant attention during the past few decades from the image processing, computational harmonic analysis, nonlinear approximation, and statistics communities. In recent years there has been a resurgence of interest in kernel-based methods, including the ubiquitous non-local means (NLM) algorithm [6], due to their practical efficacy on broad collections of "natural" images. While there is a wealth of theoretical analysis associated with nonlinear thresholding estimators based on wavelets and related sparse multiscale representations of images [13,14,35,51] or on diffusion models [52,47] and partial differential equations [39, 1], performance guarantees for NLM are lacking and this paper aims at providing some results in this direction.In this paper, we explore the theoretical underpinnings of adaptive kernel-based image estimation and derive bounds on the mean squared error as a function of the number of pixels observed and features of the underlying image. The denoising methods we consider are based on estimating each pixel value with a weighted sum of the surrounding pixels. Depending on how the weights in this average are selected, this corresponds to classical linear filters [38,60] [20,43,36] for more insights on a unifying framework for averaging filters.As none of these methods have been explicitly designed to deal with textured regions, many authors, inspired by work on texture synthesis [16] and inpainting [8], have proposed to introduce patches (small sub-images) to take advantage of natural image redundancy, es-

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“…When the noise is purely Gaussian, P(θ) = N (θ, σ 2 ), with σ known, the best estimator in terms of Mean Squared Error (or quadratic risk) is the mean, which explains the usual averaging formulation of the NL-means [5]. Recently, many authors have adopted the point of view of quadratic risk minimization as a way to optimize the parameters of the NL-means [29,39,22] or to propose further improvements [37]. In Section 4.2, we will also make use of the quadratic risk in order to compare the efficiency of different estimators in presence of impulse and Gaussian noise.…”

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confidence: 99%

“…Now, since a given pixel x belongs to several patches, multiple choices are possible to obtain a restored valueû(x) at x. This last step, called reprojection in the work of Salmon and Strozecki [37], corresponds to the general framework of estimators aggregation in statistics. Let us denote by P x a patch centered at x.…”

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confidence: 99%

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A Patch-Based Approach for Removing Impulse or Mixed Gaussian-Impulse Noise

Delon¹,

Desolneux²

2013

SIAM J. Imaging Sci.

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Abstract. In this paper, we address the problem of the restoration of images which have been affected by impulse noise or by a mixture of Gaussian and impulse noise. We rely on a patch-based approach, which requires careful choices for both the distance between patches and for the statistical estimator of the original patch. Experiments are led in the case of pure impulse noise and in the case of a mixture. The method proves to be particularly powerful, especially for the restoration of textured regions, and compares favorably to recent restoration methods.

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Patch reprojections for Non-Local methods

Cited by 48 publications

References 27 publications

PARIGI: a Patch-based Approach to Remove Impulse-Gaussian Noise from Images

PARIGI: a Patch-based Approach to Remove Impulse-Gaussian Noise from Images

Oracle Inequalities and Minimax Rates for Nonlocal Means and Related Adaptive Kernel-Based Methods

A Patch-Based Approach for Removing Impulse or Mixed Gaussian-Impulse Noise

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