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.

应用弹性成像反问题识别杨氏模量在人类生活中的弹性问题中是一个有趣的研究领域。在这项研究中，我们使用改进的输出最小二乘法确定弹性模量以解决弹性成像逆问题。研究了弹性直接问题的位移中的数值收敛。为了在优化框架中研究弹性成像逆问题，我们利用敏感性和伴随问题来概念化计算极小值梯度的新模型。然后使用模型中的离散公式来设计一种使用非线性共轭梯度方法对修改后的输出最小二乘目标函数进行有效计算梯度的方案。