Alternating method based on framelet <i>l</i><sub>0</sub>-norm and TV regularization for image restoration

Liu, Jingjing; Ni, Guoxi; Yan, Shaowen

doi:10.1080/17415977.2018.1500569

Cited by 4 publications

(2 citation statements)

References 31 publications

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“…In fact, it is typically severely illconditioned since the existence or the uniqueness of the solution are not easily ensured. Consequently, many regularization operators have been introduced to deal with the illposedness, see [35,36,41,61]. In each of those regularization approaches, the choice of the regularization parameters is very important for the computation of the a priori information about the super-resolved image.…”

Section: Parameter Learning Via Bilevel Optimization Approachmentioning

confidence: 99%

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

Laghrib,

Zahra Ait Bella,

Nachaoui

et al. 2023

Inverse Problems

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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.

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Section: Parameter Learning Via Bilevel Optimization Approachmentioning

confidence: 99%

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

Laghrib,

Zahra Ait Bella,

Nachaoui

et al. 2023

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…The field of super-resolution is of great interest due to its inherent ill-posed nature, where ensuring the existence and uniqueness of a solution is challenging. To address this problem, various regularization methods have been proposed in the literature, as discussed in references [25,24,32,44]. The selection of regularization parameters plays a crucial role in determining the quality of the super-resolved image.…”

mentioning

confidence: 99%

Learning nonlocal weights for second-order nonlocal super-resolution

Laghrib,

Bella,

Nachaoui

et al. 2023

DCDS-S

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This research introduces an enhanced approach for multiframe super-resolution (SR) that incorporates a bilevel optimization technique for learning the space variable weights parameter in the second-order nonlocal term. This novel approach effectively preserves image edges and ensures accurate reconstruction of image textures. The main contributions of this work include the establishment of the existence and uniqueness of the solution within a well-posed framework and a bilevel optimization procedure to compute the weights α. The experimental results demonstrate the efficiency and accuracy of the proposed method compared to existing super-resolution approaches. These findings highlight the practical effectiveness and potential of the proposed approach in real-world applications.

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

Afraites

Hadri

Laghrib

et al. 2020

Inverse Problems in Science and Engineering

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Alternating method based on framelet l₀-norm and TV regularization for image restoration

Cited by 4 publications

References 31 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

Learning nonlocal weights for second-order nonlocal super-resolution

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

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Alternating method based on framelet l0-norm and TV regularization for image restoration

Cited by 4 publications

References 31 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

Learning nonlocal weights for second-order nonlocal super-resolution

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

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Product

Resources

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Alternating method based on framelet l₀-norm and TV regularization for image restoration