Volume 52, Issue 4
A Nonstandard Higher-Order Variational Model for Speckle Noise Removal and Thin-Structure Detection

J. Math. Study, 52 (2019), pp. 394-424.

Published online: 2019-12

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• Abstract

We propose a multiscale approach for a nonstandard higher-order PDE based on the $p$(·)-Kirchhoff energy. We first use the topological gradient approach for a semi-linear case in order to detect important objects of the image. We consider a fully nonlinear $p$(·)-Kirchhoff equation with variable-exponent functions that are chosen adaptively based on the map provided by the topological gradient in order to preserve important features of the image. Then, we consider the split Bregman method for the numerical implementation of the proposed model. We compare our model with other classical variational approaches such as the TVL and bi-harmonic restoration models. Finally, we present some numerical results to illustrate the effectiveness of our approach.

• Keywords

Inverse problems, regularization procedures, $p$(·)-Kirchhoff, topological gradient, split Bregman.

65M32, 68U10, 35G25

hamdi.houichet@gmail.com (Hamdi Houichet)

thaljanianis@gmail.com (Anis Theljani)

maher.moakher@enit.utm.tn (Maher Moakher)

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@Article{JMS-52-394, author = {Hamdi and Houichet and hamdi.houichet@gmail.com and 5886 and Laboratory for Mathematical and Numerical Modeling in Engineering Science, University of Tunis El Manar, National Engineering School at Tunis, B.P. 37, 1002 Tunis-Belvédère, Tunisia and Hamdi Houichet and Anis and Theljani and thaljanianis@gmail.com and 5887 and Liverpool Centre for Mathematics in Healthcare, Department of Mathematical Sciences, University of Liverpool, Liverpool, UK and Anis Theljani and Badreddine and Rjaibi and badreddine.rjaibi@lamsin.rnu.tn and 5888 and Laboratory for Mathematical and Numerical Modeling in Engineering Science, University of Tunis El Manar, National Engineering School at Tunis, B.P. 37, 1002 Tunis-Belvédère, Tunisia and Badreddine Rjaibi and Maher and Moakher and maher.moakher@enit.utm.tn and 5885 and Laboratory for Mathematical and Numerical Modeling in Engineering Science, University of Tunis El Manar, National Engineering School at Tunis, B.P. 37, 1002 Tunis-Belvédère, Tunisia and Maher Moakher}, title = {A Nonstandard Higher-Order Variational Model for Speckle Noise Removal and Thin-Structure Detection}, journal = {Journal of Mathematical Study}, year = {2019}, volume = {52}, number = {4}, pages = {394--424}, abstract = {

We propose a multiscale approach for a nonstandard higher-order PDE based on the $p$(·)-Kirchhoff energy. We first use the topological gradient approach for a semi-linear case in order to detect important objects of the image. We consider a fully nonlinear $p$(·)-Kirchhoff equation with variable-exponent functions that are chosen adaptively based on the map provided by the topological gradient in order to preserve important features of the image. Then, we consider the split Bregman method for the numerical implementation of the proposed model. We compare our model with other classical variational approaches such as the TVL and bi-harmonic restoration models. Finally, we present some numerical results to illustrate the effectiveness of our approach.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v52n4.19.03}, url = {http://global-sci.org/intro/article_detail/jms/13464.html} }
TY - JOUR T1 - A Nonstandard Higher-Order Variational Model for Speckle Noise Removal and Thin-Structure Detection AU - Houichet , Hamdi AU - Theljani , Anis AU - Rjaibi , Badreddine AU - Moakher , Maher JO - Journal of Mathematical Study VL - 4 SP - 394 EP - 424 PY - 2019 DA - 2019/12 SN - 52 DO - http://doi.org/10.4208/jms.v52n4.19.03 UR - https://global-sci.org/intro/article_detail/jms/13464.html KW - Inverse problems, regularization procedures, $p$(·)-Kirchhoff, topological gradient, split Bregman. AB -

We propose a multiscale approach for a nonstandard higher-order PDE based on the $p$(·)-Kirchhoff energy. We first use the topological gradient approach for a semi-linear case in order to detect important objects of the image. We consider a fully nonlinear $p$(·)-Kirchhoff equation with variable-exponent functions that are chosen adaptively based on the map provided by the topological gradient in order to preserve important features of the image. Then, we consider the split Bregman method for the numerical implementation of the proposed model. We compare our model with other classical variational approaches such as the TVL and bi-harmonic restoration models. Finally, we present some numerical results to illustrate the effectiveness of our approach.

Hamdi Houichet, Anis Theljani, Badreddine Rjaibi & Maher Moakher. (2019). A Nonstandard Higher-Order Variational Model for Speckle Noise Removal and Thin-Structure Detection. Journal of Mathematical Study. 52 (4). 394-424. doi:10.4208/jms.v52n4.19.03
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