An improved spatially controlled reaction–diffusion equation with a non-linear second order operator for image super-resolution

Hadri, Aissam; Khalfi, Hamza; Laghrib, Amine; Nachaoui, Mourad

doi:10.1016/j.nonrwa.2021.103352

Cited by 18 publications

(6 citation statements)

References 26 publications

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“…In this section, we will show the experimental results on simulated and real images. e proposed method was compared with the state-of-the-art SR methods: BBC, bicubic interpolation of the LR reference frame; RSR [30], the robust SR method, which is based on l1norm data fidelity term and bilateral TV prior; SAR [31], TV [31], and NS [32]: the variational SR methods, which are based on Gaussian observation model and SAR, TV, and NS prior, respectively; and RDESR [28], the super-resolution method based on reaction-diffusion equation. For the NS method, filter combination NF3 was used.…”

Section: Methodsmentioning

confidence: 99%

“…e initial values of the iteration process are chosen as follows: the initial motion vectors are estimated using the LK method [44], and assuming (Λ p k ) − 1 equal to zero, a noninformative hyperprior model assumption, i.e., a θ � b θ � 0, θ ∈ Θ, the HR image is initialized using bicubic interpolation of the LR reference frame; with the above initialization and Σ s k � 0 and Σ x � 0, the parameters w and v k and the distribution of β k are initialized using equation (28), and equations ( 23) and (24), respectively. en, α is initialized using equation (26), equation (29), and equation (33) for SAR, TV, and NS prior models, respectively.…”

Section: Methodsmentioning

confidence: 99%

“…ese methods include projection onto convex sets (POCSs) [24,25], iterative back projection (IBP) [26,27], methods based on reaction-diffusion equation [28], and a group of stochastic methods, including maximum likelihood (ML) [29] and Bayesian methods [4,[30][31][32]. As pointed out in [6], robustness and flexibility in modeling noise characteristics and the prior knowledge about the solution are the major advantages of the stochastic SR approach.…”

Section: Introductionmentioning

confidence: 99%

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A Robust Multiframe Image Super-Resolution Method in Variational Bayesian Framework

Min

Fan

2022

Mathematical Problems in Engineering

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Multiframe image super-resolution (MISR) combines complementary information of a set of low-resolution (LR) images to reconstruct a high-resolution (HR) one. In this study, we propose a robust and fully data-driven MISR method in the variational Bayesian framework. Different from the existing variational super-resolution (SR) methods, we use the l1 norm-based observation model, which takes the acquisition noise, outliers, and impulse noise into account. Furthermore, we have evaluated three typical image prior models, and the most appropriate one is chosen for our proposed method. The proposed method has the following advantages: (1) the HR image and all parameters are automatically estimated in an optimal stochastic sense; (2) the algorithm is robust to impulse noise and outliers. Extensive experiments with synthetic and real images demonstrate the advantages of the proposed method.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Robust Multiframe Image Super-Resolution Method in Variational Bayesian Framework

Min

Fan

2022

Mathematical Problems in Engineering

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“…Use of the van Cittert algorithm and Wiener filter can be seen in [50]. Statistical [51,52] and various nonlinear methods [53,54] are also used.…”

Section: Deconvolution Methods Classificationmentioning

confidence: 99%

State-of-the-Art Approaches for Image Deconvolution Problems, including Modern Deep Learning Architectures

Makarkin

Bratashov

2021

Micromachines

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In modern digital microscopy, deconvolution methods are widely used to eliminate a number of image defects and increase resolution. In this review, we have divided these methods into classical, deep learning-based, and optimization-based methods. The review describes the major architectures of neural networks, such as convolutional and generative adversarial networks, autoencoders, various forms of recurrent networks, and the attention mechanism used for the deconvolution problem. Special attention is paid to deep learning as the most powerful and flexible modern approach. The review describes the major architectures of neural networks used for the deconvolution problem. We describe the difficulties in their application, such as the discrepancy between the standard loss functions and the visual content and the heterogeneity of the images. Next, we examine how to deal with this by introducing new loss functions, multiscale learning, and prior knowledge of visual content. In conclusion, a review of promising directions and further development of deconvolution methods in microscopy is given.

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“…Nevertheless, many algorithms are developed, dissjointly for different area, to deal with non-smooth non-convex optimization [1,3,25,40]. Otherwise, to reduce the undesirable staircase effect, high order PDEs have been employed [20,22,44] in the denoising context. These equations can reduce the staircase effect.…”

Section: Introductionmentioning

confidence: 99%

A non-convex PDE-constrained denoising model for impulse and Gaussian noise mixture reduction

Laghrib

Afraites

Hadri

et al. 2023

IPI

Self Cite

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<p style='text-indent:20px;'>This paper introduces a novel optimization procedure to reduce a mixture of Gaussian and impulse noise from images. This framework is based on a non-convex PDE-constrained with two diffusion operators: a local weickert and a fractional-order ones. The non-convex norm is applied to remove the impulse component, while the local and fractional operators are introduced to preserve image texture and edges. In the first part, we study the theoretical properties of the proposed PDE-constrained, and we show some well-posedness results. In a second part, after having demonstrated how to numerically find a minimizer, a proximal linearized algorithm combined with a Primal-Dual approach is introduced with local convergence results. Finally, we show extensive denoising experiments on various images and noise intensities which confirms the validity of the non-convex PDE-constrained, its analysis and also the proposed optimization procedure.</p>

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An improved spatially controlled reaction–diffusion equation with a non-linear second order operator for image super-resolution

Cited by 18 publications

References 26 publications

A Robust Multiframe Image Super-Resolution Method in Variational Bayesian Framework

A Robust Multiframe Image Super-Resolution Method in Variational Bayesian Framework

State-of-the-Art Approaches for Image Deconvolution Problems, including Modern Deep Learning Architectures

A non-convex PDE-constrained denoising model for impulse and Gaussian noise mixture reduction

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