Quantitative elastography, solving the inverse elasticity problem using the Gauss-Newton method.

This work presents the application of a constrained Gauss Newton method for the solution of an inverse elasticity problem in ultrasound elastography. This algorithm was written taking care of real constraints, like the limited and noisy data used to estimate the volumepsilas properties and the speed necessary to have a real time application in a real medical environment. The algorithm is tested on data acquired on polyvinyl alcohol (PVA) phantoms. The role of the amount of elements used to discretized the volume, the role of the regularization and the role of noise are investigated. The possible application of the algorithm is in the use of quantitative elastography as tactile sensor for tactile feedback in minimally invasive surgery.