A linearly convergent algorithm without prior knowledge of operator norms for solving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e334" altimg="si2.svg"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo linebreak="goodbreak" linebreakstyle="after">−</mml:mo><mml:msub><mml:mrow><mml:mi>ℓ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> minimization

Zhuang, Yaru; Che, Haitao; Chen, Haibin

doi:10.1016/j.aml.2021.107717

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…This is a typical 2 − 1 denoising problem [6], which can be solved directly by the soft threshold method using ( 24)…”

Section: A Derivative Fidelity-based Total Generalized Variation Meth...mentioning

confidence: 99%

“…Because the function in (2) is both simple and easily computable, Tikhonov regularization is widely used, but there are problems of excessive smoothness and failure to save key secondary details. 1 regularization [6] uses Φ(u) = u 1 , which is the sum matrix of the absolute values of each element in the image. The presence of the 1 term encourages small components of u to become exactly zero, generating sparse solutions.…”

Section: Introductionmentioning

confidence: 99%

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A Derivative Fidelity-Based Total Generalized Variation Method for Image Restoration

Zou

et al. 2022

Mathematics

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Image edge is the most indicative feature that forms a significant role in image analysis and image understanding, but edge-detail preservation is a difficult task in image restoration due to noise and blur during imaging. The balance between edge preservation and noise removal has always been a difficult problem in image restoration. This paper proposes a derivative fidelity-based total generalized variation method (D-TGV) to improve this balance. First, an objective function model that highlights the ability to maintain details is proposed for the image restoration problem, which is combined with a fidelity term in derivative space and a total generalized variation regularization term. This is designed to achieve the advantage of preserving details in derivative space and eliminate the staircase effect caused by traditional total variation. Second, the alternating direction method of the multipliers (ADMM) is used to solve the model equations by decomposing the original, highly complex model into several simple sub-problems to attain rapid convergence. Finally, a series of experiments conducted on standard grayscale images showed that the proposed method exhibited a good balance between detail preservation and denoising but also reached completion with the fewest iterations compared with the currently established methods.

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“…This is a typical 2 − 1 denoising problem [6], which can be solved directly by the soft threshold method using ( 24)…”

Section: A Derivative Fidelity-based Total Generalized Variation Meth...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Derivative Fidelity-Based Total Generalized Variation Method for Image Restoration

Zou

et al. 2022

Mathematics

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Second order self-adaptive dynamical system for sparse signal reconstruction and applications to image recovery

Che

Liu

Chen

et al. 2023

Applied Mathematics and Computation

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Sparse representation of guided wave signals with differential norm penalty

Chen,

Zhang,

et al. 2024

Knowledge-Based Systems

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A linearly convergent algorithm without prior knowledge of operator norms for solving ℓ1−ℓ2 minimization

Cited by 4 publications

References 22 publications

A Derivative Fidelity-Based Total Generalized Variation Method for Image Restoration

A Derivative Fidelity-Based Total Generalized Variation Method for Image Restoration

Second order self-adaptive dynamical system for sparse signal reconstruction and applications to image recovery

Sparse representation of guided wave signals with differential norm penalty

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