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Proceedings ArticleDOI

Gradient sensitive kernel for Image Denoising, using Gaussian Process Regression

TL;DR: The focus is primarily on the design of a local gradient sensitive kernel that captures pixel similarity in the context of image Denoising that gives better PSNR values in comparison to existing popular denoising techniques.
Abstract: We target the problem of Image Denoising using Gaussian Processes Regression (GPR). Being a non-parametric regression technique, GPR has received much attention in the recent past and here we further explore its versatility by applying it to a denoising problem. The focus is primarily on the design of a local gradient sensitive kernel that captures pixel similarity in the context of image denoising. This novel kernel formulation is used to shape the smoothness of the joint GP prior. We apply the GPR denoising technique to small patches and then stitch back these patches, this allows the priors to be local and relevant, also this helps us in dealing with GPR complexity. We demonstrate that our GPR based technique gives better PSNR values in comparison to existing popular denoising techniques.
Citations
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References
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Proceedings ArticleDOI
04 Jan 1998
TL;DR: In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception.
Abstract: Bilateral filtering smooths images while preserving edges, by means of a nonlinear combination of nearby image values. The method is noniterative, local, and simple. It combines gray levels or colors based on both their geometric closeness and their photometric similarity, and prefers near values to distant values in both domain and range. In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception. Also, in contrast with standard filtering, bilateral filtering produces no phantom colors along edges in color images, and reduces phantom colors where they appear in the original image.

8,738 citations


"Gradient sensitive kernel for Image..." refers background in this paper

  • ...This kernel can be related to the bilateral Kernel introduced in [17] which measures both spatial and radiometric distances....

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Journal ArticleDOI
TL;DR: An algorithm based on an enhanced sparse representation in transform domain based on a specially developed collaborative Wiener filtering achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.
Abstract: 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 2D image fragments (e.g., blocks) into 3D data arrays which we call "groups." Collaborative Altering is a special procedure developed to deal with these 3D groups. We realize it using the three successive steps: 3D transformation of a group, shrinkage of the transform spectrum, and inverse 3D transformation. The result is a 3D 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.

7,912 citations


"Gradient sensitive kernel for Image..." refers background or methods in this paper

  • ...Mostly these denoising techniques are aimed at a particular noise model [4], [14] and thus do not effectively capture the real life complex noise models....

    [...]

  • ...techniques that are being actively pursued include waveletbased methods [4], [14], neighborhood filters based methods [1], methods based on Partial Differential Equations [11], and fractal theory based methods [6]....

    [...]

  • ...State-of-art generative models usually combine different sources to achieve better results [4], [7]....

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Proceedings ArticleDOI
20 Jun 2005
TL;DR: A new measure, the method noise, is proposed, to evaluate and compare the performance of digital image denoising methods, and a new algorithm, the nonlocal means (NL-means), based on a nonlocal averaging of all pixels in the image is proposed.
Abstract: We propose a new measure, the method noise, to evaluate and compare the performance of digital image denoising methods. We first compute and analyze this method noise for a wide class of denoising algorithms, namely the local smoothing filters. Second, we propose a new algorithm, the nonlocal means (NL-means), based on a nonlocal averaging of all pixels in the image. Finally, we present some experiments comparing the NL-means algorithm and the local smoothing filters.

6,804 citations


"Gradient sensitive kernel for Image..." refers methods in this paper

  • ...Taking inspiration from NL-means [2] he designed a Kernel which measured both spatial and...

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  • ...Taking inspiration from NL-means [2] he designed a Kernel which measured both spatial and neighborhood similarity....

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Journal ArticleDOI
TL;DR: A general mathematical and experimental methodology to compare and classify classical image denoising algorithms and a nonlocal means (NL-means) algorithm addressing the preservation of structure in a digital image are defined.
Abstract: 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, m

4,153 citations


"Gradient sensitive kernel for Image..." refers background or methods in this paper

  • ...techniques that are being actively pursued include waveletbased methods [4], [14], neighborhood filters based methods [1], methods based on Partial Differential Equations [11], and fractal theory based methods [6]....

    [...]

  • ...Similar kernels have found application in other well-known denoising techniques [1]....

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Journal ArticleDOI
TL;DR: The performance of this method for removing noise from digital images substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
Abstract: We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.

2,439 citations


"Gradient sensitive kernel for Image..." refers background or methods in this paper

  • ...Mostly these denoising techniques are aimed at a particular noise model [4], [14] and thus do not effectively capture the real life complex noise models....

    [...]

  • ...Markov Random Field based pixel similarity models [3], [12], or patch-based mixture models [14] are popular approaches [18]....

    [...]

  • ...techniques that are being actively pursued include waveletbased methods [4], [14], neighborhood filters based methods [1], methods based on Partial Differential Equations [11], and fractal theory based methods [6]....

    [...]