Nonlinear conjugate gradient method for identifying Young's modulus of the elasticity imaging inverse problem

Abstract

Application of elasticity imaging inverse problem to identify Young's modulus in the elasticity problems in human's life is an interesting research area. In this study, we identify the modulus of elasticity for solving elasticity imaging inverse problem using a modified output least-squares method. Numerical convergence in the displacements of the direct problem for elasticity is investigated. To study the elasticity imaging inverse problem in an optimization framework, we utilize the sensitivity and adjoint problems to conceptualize a new model for computing the gradient of the minimizer. Discrete formulae in the model are then used to devise a scheme for an efficient computation gradient of the modified output least-squares objective function using the nonlinear conjugate gradient method. Numerical experiments demonstrate the effectiveness of the proposed technique.

Keywords:

• Identification problems
• elasticity imaging inverse problem
• modified output least squares
• nonlinear conjugate gradient method

2010 Mathematics Subject Classifications:

• 65N20
• 65N30
• 65N21

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Science and Technology Development Fund (STDF) of Egypt, project No: 39385. This research was supported in part by the National Key R&D Program of China under P2018YFE0198400, Shenzhen [grant number ZDSYS201703031711426], [grant number JCYJ20170818153840322], and NFSC [grant number 12071461].