Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problem

Talaat Abdelhamid; F. Khayat; H. Zayeni; Rongliang Chen; Talaat Abdelhamid; F. Khayat; H. Zayeni; Rongliang Chen

doi:10.3934/era.2022079

Electronic Research Archive

2022, Volume 30, Issue 4: 1532-1557. doi: 10.3934/era.2022079

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Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problem

1.
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China
2.
Physics and Mathematical Engineering Department, Faculty of Electronic Engineering, Menoufiya University, Menouf 32952, Egypt
3.
Center for Turbulence and Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
4.
University of Tunis El Manar, National Engineering School of Tunis, LAMSIN 1002, Tunis, Tunisia

Academic Editor: Jingzhi Li

Received: 31 December 2021 Revised: 25 February 2022 Accepted: 07 March 2022 Published: 23 March 2022

The present study focuses on reconstructing the Young's modulus for the elasticity imaging inverse problem. It is a very interesting and challenging problem encountered in tumor detection where the variation of the elastic properties of soft tissues allows to distinguish between normal and diseased tissues. The Levenberg-Marquardt method is used to treat this ill-posed inverse problem and the non-convex minimization is changed into a convex one. We get an explicit expression for computing the descent direction. The proposed technique with a constant and space dependant coefficients and for various real materials is examined. The obtained results of the 2D and 3D view for the reconstructed Young's modulus are agree with those of the exact coefficients. The proposed algorithm is implemented for different levels of noise in the data.
- identification problems,
- elasticity imaging inverse problem,
- Levenberg-Marquardt method,
- Young's modulus,
- least-squares problem
Citation: Talaat Abdelhamid, F. Khayat, H. Zayeni, Rongliang Chen. Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problem[J]. Electronic Research Archive, 2022, 30(4): 1532-1557. doi: 10.3934/era.2022079

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Abstract

The present study focuses on reconstructing the Young's modulus for the elasticity imaging inverse problem. It is a very interesting and challenging problem encountered in tumor detection where the variation of the elastic properties of soft tissues allows to distinguish between normal and diseased tissues. The Levenberg-Marquardt method is used to treat this ill-posed inverse problem and the non-convex minimization is changed into a convex one. We get an explicit expression for computing the descent direction. The proposed technique with a constant and space dependant coefficients and for various real materials is examined. The obtained results of the 2D and 3D view for the reconstructed Young's modulus are agree with those of the exact coefficients. The proposed algorithm is implemented for different levels of noise in the data.

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