A nonstandard higher-order variational model to speckle noise removal and thin-structure detection

Houichet, Hamdi, Theljani, Anis, Moakher, Maher and Rjaibi, Badreddine (2017) A nonstandard higher-order variational model to speckle noise removal and thin-structure detection. Journal of Mathematical Study, 52 (4). pp. 394-424.

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Official URL: http://dx.doi.org/10.4208/jms.v52n4.19.03

Abstract

In this work, we propose a multiscale approach for a nonstandard higher-order PDE based on the $p(\cdot)$-Kirchhoff energy. First, we consider a topological gradient approach for a semilinear case in order to detect important object of image. Then, we consider a fully nonlinear $p(\cdot)$-Kirchhoff equation with variables exponent functions that are chosen adaptively based on the map furnished 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 our proposed model. We compare our model with other classical variational approaches such that the TVL and biharmonic restoration models. Finally, we present some numerical results to illustrate the effectiveness of our approach.

Item Type:	Article
Additional Information:	The work is not completed yet
Uncontrolled Keywords:	math.NA, math.NA, math.AP
Depositing User:	Symplectic Admin
Date Deposited:	29 Jun 2017 08:27
Last Modified:	19 Jan 2023 07:02
DOI:	10.4208/jms.v52n4.19.03
Open Access URL:	https://arxiv.org/pdf/1706.06190.pdf
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3008179