Reverse weak formulation for parameters identification – REWARD

The main goal of the project REWARD is to deepen and broaden the analysis of a recently introduced method for recovering elastic properties of materials from internal displacement data and to extend it for other applications.
Instead of inverting a non-linear forward operator, the heart of the method is to write the coefficients to recover as the solution of a linear system via a "reverse weak formulation".
We have analyzed the method, proved the stability of the inverse problem and successfully applied the method to experimental data in the case of quasistatic ultrasound elastography experiments.
We aim at proving stability estimates for the general theoretical problem and its discretization. We shall introduce a new stochastic framework and extend the method to visco-elastic models. We will test the method on various types of experimental data obtained from state of the art imaging technics.