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

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.