Image Denoising by Median Filter in Wavelet Domain

Ramadhan, Afrah; Mahmood, Firas; Elçi, Atilla

doi:10.5121/ijma.2017.9104

Cited by 19 publications

(25 citation statements)

References 11 publications

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“…Traditional methods for estimating the regularization parameter generally depend on the signal-to-noise ratio and on the image statistics [56]. For most applications the noise level is unknown and can be estimated, for instance, by applying a median filter over the wavelet diagonal coefficients of the image [57]. This strategy is used in the numerical experiments presented in Section 6.…”

Section: Hidden Structuresmentioning

confidence: 99%

“…Similarly, for MLP and PDHG, the authors do not provide models that were trained specifically for MotionB and Square, so, in order to test these methods on MotionB we use the same models as for MotionA, and for Square we use models that were trained for a larger uniform blur. Since MLP, EPLL and IRCNN require the knowledge of the noise level, for the GaussianB degradation model, we make use of the estimation of the noise standard deviation given by the method in [57]. In addition, since some comparison methods, like EPLL for instance, do not estimate well the borders of the images, the SSIM index is computed excluding a 6-pixel-wide frame for all images and all tested methods.…”

Section: Evaluation Metrics and Competitorsmentioning

confidence: 99%

See 1 more Smart Citation

Deep unfolding of a proximal interior point method for image restoration

Bertocchi¹,

Chouzenoux²,

Corbineau³

et al. 2020

Inverse Problems

109

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Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters, which can be estimated through computationally expensive and timeconsuming methods. In contrast, deep learning offers very generic and efficient architectures, at the expense of explainability, since it is often used as a black-box, without any fine control over its output. Deep unfolding provides a convenient approach to combine variational-based and deep learning approaches. Starting from a variational formulation for image restoration, we develop iRestNet, a neural network architecture obtained by unfolding a proximal interior point algorithm. Hard constraints, encoding desirable properties for the restored image, are incorporated into the network thanks to a logarithmic barrier, while the barrier parameter, the stepsize, and the penalization weight are learned by the network. We derive explicit expressions for the gradient of the proximity operator for various choices of constraints, which allows training iRestNet with gradient descent and backpropagation. In addition, we provide theoretical results regarding the stability of the network for a common inverse problem example. Numerical experiments on image deblurring problems show that the proposed approach compares favorably with both state-of-the-art variational and machine learning methods in terms of image quality.

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Section: Hidden Structuresmentioning

confidence: 99%

Section: Evaluation Metrics and Competitorsmentioning

confidence: 99%

Deep unfolding of a proximal interior point method for image restoration

Bertocchi¹,

Chouzenoux²,

Corbineau³

et al. 2020

Inverse Problems

109

View full text Add to dashboard Cite

show abstract

“…The resultant solution of equations (7) and (8) through interpolation gives matrix system of (M +N )×(M +N ) equations which is given as under.…”

Section: B Radial Basis Function Approximationmentioning

confidence: 99%

“…where z: ⊂ R −→ R 2 represents the given true image, z 0 is the noisy image with additive noise η. In literature, various nonlinear approaches have been utilized to tackle this problem, such as wavelet approaches [2]- [4], adaptive smoothing [5], [6], stochastic approaches [7], [8], anisotropic diffusion [9], [10]. Recently variational approaches have also been utilized to solve such problem, for instance [11]- [13].…”

Section: Introductionmentioning

confidence: 99%

Total Variation Filter via Multiquadric Radial Basis Function Approximation Scheme for Additive Noise Removal

Khan¹,

Altamimi

Khan

et al. 2020

IEEE Access

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The Digital Total Variation (DTV) scheme is a digitized energy regularization scheme used for image denoising. This technique takes advantage of being applied to arbitrarily located data points and also has the edge detective property. This article aims to introduce a novel meshless scheme using DTV filtering and Radial Basis Functions (RBFs) to solve the associated equation with the DTV model numerically which results in the image denoising to remove additive noise from image information. This meshless algorithm based on local collocation and Multiquadric Radial Basis Function. These appearances allow this algorithm not only to remove the additive noise from images but also to resolve the discontinuities sharply. It is also noticed that the proposed meshless scheme is simple, fast, computationally effective, requires simply post-processing, and can be easily implemented mathematically. Experimental results confirm that the peak signal-to-noise ratio, the structural similarity, signal-to-noise ratio, the visual effect, and the computational performance of this new meshless scheme are improved compared with state-of-the-art denoising schemes. Furthermore, the proposed scheme can be applied to colour images as well.

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“…The barrier parameter is obtained using two convolutional layers followed by a fully connected layer, as depicted in Figure 2. The regularization parameter λ k is inferred from the image statistics and the following estimation of the noise level [26],…”

Section: Hidden Structuresmentioning

confidence: 99%

Learned Image Deblurring by Unfolding a Proximal Interior Point Algorithm

Corbineau

Bertocchi

Chouzenoux

et al. 2019

2019 IEEE International Conference on Image Processing (ICIP)

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Image restoration is frequently addressed by resorting to variational methods which account for some prior knowledge about the solution. The success of these methods, however, heavily depends on the estimation of a set of hyperparameters. Deep learning architectures are, on the contrary, very generic and efficient, but they offer limited control over their output. In this paper, we present iRestNet, a neural network architecture which combines the benefits of both approaches. iRestNet is obtained by unfolding a proximal interior point algorithm. This enables enforcing hard constraints on the pixel range of the restored image thanks to a logarithmic barrier strategy, without requiring any parameter setting. Explicit expressions for the involved proximity operator, and its differential, are derived, which allows training iRestNet with gradient descent and backpropagation. Numerical experiments on image deblurring show that the proposed approach provides good image quality results compared to state-of-theart variational and machine learning methods.

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Image Denoising by Median Filter in Wavelet Domain

Abstract: ABSTRACT

Cited by 19 publications

References 11 publications

Deep unfolding of a proximal interior point method for image restoration

Deep unfolding of a proximal interior point method for image restoration

Total Variation Filter via Multiquadric Radial Basis Function Approximation Scheme for Additive Noise Removal

Learned Image Deblurring by Unfolding a Proximal Interior Point Algorithm

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