A PDE variational approach to image denoising and restoration

Barbu, Tudor; Barbu, Viorel; Biga, Veronica; Coca, Daniel

doi:10.1016/j.nonrwa.2008.01.017

Cited by 56 publications

(24 citation statements)

References 8 publications

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“…In our previous works one considered smoothing techniques for grayscale digital images affected by other types of noise [1][2][3].…”

Section: Discussionmentioning

confidence: 99%

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Novel Linear Image Denoising Approach Based on a Modified Gaussian Filter Kernel

Barbu

2012

Numerical Functional Analysis and Optimization

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A Gaussian noise reduction technique for grayscale images is proposed in this article. It uses a modified Gaussian filter kernel based on a hyperbolic second-order equation. The introduced mathematical model differs from the classic Gaussian model provided by the heat equations, by a localization property. Our filtering approach reduces the amount of Gaussian noise and alsoenhances the image contrast. Some image denoising experiments that prove the effectiveness of the proposed method are also described in this article.

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“…In our previous works one considered smoothing techniques for grayscale digital images affected by other types of noise [1][2][3].…”

Section: Discussionmentioning

confidence: 99%

“…We proposed various PDE-based models for noise removal and image restoration in our previous works [1][2][3]. Herein we propose a PDEbased image enhancement technique using an improved Gaussian filter kernel.…”

Section: Introductionmentioning

confidence: 99%

Novel Linear Image Denoising Approach Based on a Modified Gaussian Filter Kernel

Barbu

2012

Numerical Functional Analysis and Optimization

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“…Barbu et al [20] discussed a general variational model for image denoising and restoration based on minimization of a convex function of the gradient under minimal growth conditions.…”

Section: Barbu Methodsmentioning

confidence: 99%

Efficient diffusion coefficient for image denoising

Rafsanjani

Sedaaghi

Saryazdi

2016

Computers & Mathematics with Applications

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a b s t r a c tDiffusion coefficient has an important role in the performance of partial differential equation (PDE) based image denoising techniques. Commonly, the classical Perona-Malik (PM) diffusion coefficient is widely used in PDE-based noise removal algorithms. In this paper, PM diffusion coefficient is analyzed regarding to its flux. Based on the analysis, PM flux for regions where the gradient magnitude is higher than smoothing threshold may lead to undesirable blurring effect and edge displacement. To address these issues, the image is divided into three segments based on the gradient magnitude: regions where the gradient is lower than the smoothing threshold, regions where the gradient is between the smoothing threshold and inflection point of flux, and regions where the gradient magnitude is higher than inflection point. We define the conditions that should be considered in these three segments. Then, a diffusion coefficient, satisfying all these conditions, is computed. Experimental results confirm the performance of the proposed method with regard to peak signal-to-noise ratio (PSNR), mean structural similarity (MSSIM), universal quality index (UQI), visual information fidelity (VIF), feature similarity (FSIM), information content weighted SSIM (IW-SSIM) and visual quality.

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“…The basic formula of the Gabor filter, a combination of the Gaussian kernel with trigonometric function extracting features, is drawn by Equations (13) and (14), [21].…”

Section: Feature Extractionmentioning

confidence: 99%

“…′ are jets i of the graphs ‫ܩ‬ ܽ݊݀ ‫ܩ‬ ′ respectively, ܽ ܽ݊݀ ߙ ‫݁ݎܽ‬ the results of Gabor filter, ݊ ‫ݏ݅‬ the number of the nodes for each graph and ܰ ‫ݏ݅‬ the number of Gabor filter [21].…”

Section: Matching Setmentioning

confidence: 99%