| Author | Baasansuren Jadamba, Akhtar A. Khan, Assad A. Oberai, and Miguel Sama |
|---|---|
| Title | First-Order and Second-Order Adjoint Methods for Parameter Identification Problems with an Application to the Elasticity Imaging Inverse Problem |
| Year | 2017 |
| Journal | Inverse Problems in Science and Engineering |
| Abstract | We devise a fast and reliable computational framework for the elasticity imaging inverse problem of detecting cancerous tumors in the human body using an output least-squares (OLS) approach. From a mathematical standpoint, this inverse problem requires identifying a parameter in a mixed variational problem. We develop, in a continuous setting, a first-order adjoint method and two second-order adjoint methods. The continuous formulae are then used to devise a scheme for an efficient computation of the gradient and the Hessian of the OLS objective. We give detailed numerical examples. |