Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problem
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 dise...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022079?viewType=HTML |
| _version_ | 1811235208598388736 |
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| author | Talaat Abdelhamid F. Khayat H. Zayeni Rongliang Chen |
| author_facet | Talaat Abdelhamid F. Khayat H. Zayeni Rongliang Chen |
| author_sort | Talaat Abdelhamid |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T11:47:09Z |
| format | Article |
| id | doaj.art-65c099b4b94c47ef9e0bcce4eead56f7 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-12T11:47:09Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-65c099b4b94c47ef9e0bcce4eead56f72022-12-22T03:34:19ZengAIMS PressElectronic Research Archive2688-15942022-03-013041532155710.3934/era.2022079Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problemTalaat Abdelhamid 0F. Khayat 1H. Zayeni2Rongliang Chen31. 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, China4. University of Tunis El Manar, National Engineering School of Tunis, LAMSIN 1002, Tunis, Tunisia4. University of Tunis El Manar, National Engineering School of Tunis, LAMSIN 1002, Tunis, Tunisia1. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, ChinaThe 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.https://www.aimspress.com/article/doi/10.3934/era.2022079?viewType=HTMLidentification problemselasticity imaging inverse problemlevenberg-marquardt methodyoung's modulusleast-squares problem |
| spellingShingle | Talaat Abdelhamid F. Khayat H. Zayeni Rongliang Chen Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problem Electronic Research Archive identification problems elasticity imaging inverse problem levenberg-marquardt method young's modulus least-squares problem |
| title | Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problem |
| title_full | Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problem |
| title_fullStr | Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problem |
| title_full_unstemmed | Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problem |
| title_short | Levenberg-Marquardt method for identifying Young's modulus of the elasticity imaging inverse problem |
| title_sort | levenberg marquardt method for identifying young s modulus of the elasticity imaging inverse problem |
| topic | identification problems elasticity imaging inverse problem levenberg-marquardt method young's modulus least-squares problem |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022079?viewType=HTML |
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