Nonlinear estimation of the lateral displacement using tissue incompressibility

Using the incompressibility property of soft tissue, high quality lateral displacement distributions can be reconstructed from accurate axial displacement measurements and noisy lateral displacement estimates. Previous methods appropriate for small deformations have been extended for high magnitude deformations requiring a nonlinear model. Problems arising in incompressibility processing for large deformations are considered. Applications of nonlinear incompressibility methods to ultrasonic measurements on gel-based, tissue equivalent phantoms are given. Lateral displacement images reconstructed with nonlinear methods are compared to those reconstructed with linear methods for both small and large deformations.