A high order PDE-constrained optimization for the image denoising problem

Afraites, Lekbir; Hadri, Aissam; Laghrib, Amine; Nachaoui, Mourad

doi:10.1080/17415977.2020.1867547

Cited by 25 publications

(6 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These three contributions collectively enhance our understanding of the inverse imaging problem addressed in (1). We provide mathematical and computational insights to ensure a valid and effective solution, while also enabling the determination of the optimal balance between regularization and data fidelity.…”

Section: Introductionmentioning

confidence: 87%

Bilevel optimal parameter learning for a high-order nonlocal multiframe super-resolution problem

Laghrib,

Zahra Ait Bella,

Nachaoui

et al. 2023

Inverse Problems

Self Cite

View full text Add to dashboard Cite

This work elaborated an improved method to multiframe super-resolution (SR), which involves a nonlocal first-order regularization combined with a nonlocal p-Laplacian term. The nonlocal TV term excels at edge preserving, whilst the nonlocal p-Laplacian is commonly used to perfectly reconstruct image textures. Firstly, we discuss the existence and uniqueness of a solution to our new model in a well posed framework. Then, we derive a modified Primal-dual iteration to compute the super-resolved solution. Furthermore, we introduce a new bilevel optimization approach to learn two regularization parameters. The included tests validate that the introduced optimization procedure performs favorably compared to numerous SR approaches in terms of efficiency and accuracy.

show abstract

Section: Introductionmentioning

confidence: 87%

Bilevel optimal parameter learning for a high-order nonlocal multiframe super-resolution problem

Laghrib,

Zahra Ait Bella,

Nachaoui

et al. 2023

Inverse Problems

Self Cite

View full text Add to dashboard Cite

show abstract

“…R(u) is a regularization term representing a prior knowledge on u and δ is the regularization parameter. The resolution of the minimization problem (1) can be obtained through optimization methods [17,1,22], or using the Euler-Lagrange equation associated with the minimization problem (1). Recently, El Mourabit et al [7], proposed a new nonlinear PDE that enhance the coherence property and avoids blur.…”

Section: 1mentioning

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

Self Cite

View full text Add to dashboard Cite

<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>

show abstract

“…in the variational formulation of mechanical problems whenever nonconvex energy functionals (non-smooth constitutive laws) are involved [3,4]. However, more of their mathematical and applied developments can be found in [5][6][7] and the reference therein. In the last years, inverse problems have grown in popularity as a subject of applied mathematics with numerous practical applications [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Hemivariational inverse problem for contact problem with locking materials

Faiz¹,

Baiz²,

Benaissa³

et al. 2021

Math. Model. Comput.

View full text Add to dashboard Cite

The aim of this work is to study an inverse problem for a frictional contact model for locking material. The deformable body consists of electro-elastic-locking materials. Here, the locking character makes the solution belong to a convex set, the contact is presented in the form of multivalued normal compliance, and frictions are described with a sub-gradient of a locally Lipschitz mapping. We develop the variational formulation of the model by combining two hemivariational inequalities in a linked system. The existence and uniqueness of the solution are demonstrated utilizing recent conclusions from hemivariational inequalities theory and a fixed point argument. Finally, we provided a continuous dependence result and then we established the existence of a solution to an inverse problem for piezoelectric-locking material frictional contact problem.

show abstract

A high order PDE-constrained optimization for the image denoising problem

Cited by 25 publications

References 55 publications

Bilevel optimal parameter learning for a high-order nonlocal multiframe super-resolution problem

Bilevel optimal parameter learning for a high-order nonlocal multiframe super-resolution problem

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

Hemivariational inverse problem for contact problem with locking materials

Contact Info

Product

Resources

About