A nonlinear fourth-order PDE for multi-frame image super-resolution enhancement

Laghrib, Amine; Chakib, Abdelkrim; Hadri, Aissam; Hakim, Abdelilah

doi:10.3934/dcdsb.2019188

Cited by 6 publications

(3 citation statements)

References 66 publications

(109 reference statements)

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“…Fourth-order PDEs are very useful in different fields of science, such as engineering [42][43][44], signal processing [45][46][47][48], nuclear physics [49,50], etc. As an example, these kind of PDEs arise in traveling waves of suspension bridges.…”

Section: Introductionmentioning

confidence: 99%

Eigenvalue of (p,q)-Biharmonic System along the Ricci Flow

Yan,

Li,

Saha

et al. 2024

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Section: Introductionmentioning

confidence: 99%

Eigenvalue of (p,q)-Biharmonic System along the Ricci Flow

Yan,

Li,

Saha

et al. 2024

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“…However, when the blur and noise levels are too high, the obtained HR image still contains some artefacts, in particular the blur. More recently a fourth-order nonlinear PDE has been introduced with much more constrained diffusion that stops the edges destruction and preserve the smooth areas and texture [30]. In contrast, the blur apparition problem is still a remaining weakness of this PDE.…”

Section: Introductionmentioning

confidence: 99%

An improved PDE-constrained optimization fluid registration for image multi-frame super resolution

et al. 2022

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The main idea of multi-frame super resolution (SR) algorithms is to recover a single high-resolution image from a sequence of low resolution ones of the same object. The success of the SR approaches is often related to a well registration and restoration steps. Therefore, we propose a new approach based on a partial differential equation (PDE)-constrained optimization fluid image registration and we use a fourth order PDE to treat both the registration and restoration steps that guarantee the success of SR algorithms. Since the registration step is usually a variational ill-posed model, a mathematical study is needed to check the existence of the solution to the regularized problem. Thus, we prove the existence and of the well posed fluid image registration and assure also the existence of the used second order PDE in the restoration step. The results show that the proposed method is competitive with the existing methods.

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“…However, when the blur and noise levels are too high, the obtained HR image still contains some artefacts, in particular the blur. More recently a fourth-order nonlinear PDE is then introduced with much more constrained diffusion that stops the edges destruction and preserves the smooth areas and texture [11]. In contrast, the blur apparition problem is still a remaining weakness of this PDE.…”

mentioning

confidence: 99%

On the well-posedness of a tensor-based second order PDE with bilateral term for image super-resolution

Idriss

Hakim

Laghrib

2023

EECT

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<p style='text-indent:20px;'>In this paper, we introduce a second-order equation based on a diffusion tensor combined with a bilateral total variation (BTV) term that takes the benefit from the diffusion model of Perona-Malik in the homogeneous regions, the Weickert model near sharp edge and the BTV term in reducing blur. Compared to the other partial differential equations (PDE) used in the SR context, the proposed super-resolution (SR) PDE can efficiently preserve image components such as corners and flat regions with less apparition of blur in homogeneous regions. Moreover, since the SR approaches are always ill-posed, a mathematical study of the existence and uniqueness of the solution is also checked in a Sobolev space. From the numerical experiments we can observe that the proposed PDE can efficiently improve the quality of the high-resolution (HR) image. Surprisingly, the apparition of blur in the restored image is less compared to the other methods. In addition to visual evaluation, two-based metrics are computed to confirm the improvements offered by the proposed PDE.</p>

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A nonlinear fourth-order PDE for multi-frame image super-resolution enhancement

Cited by 6 publications

References 66 publications

Eigenvalue of (p,q)-Biharmonic System along the Ricci Flow

Eigenvalue of (p,q)-Biharmonic System along the Ricci Flow

An improved PDE-constrained optimization fluid registration for image multi-frame super resolution

On the well-posedness of a tensor-based second order PDE with bilateral term for image super-resolution

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