Wave equation based transmission tomography

For iterative image reconstruction of transmission tomography we apply the paraxial approximation of the Helmholtz equation for a spherical transducer arrangement. We choose this approach due to its three order of magnitude lower complexity than full wave solutions with the same precision for transmission tomography. In homogeneous media we prove that our forward solution is exact. With the help of this forward solution 2D and 3D ultrasound measurements could be simulated for transmission tomography. 2D reconstructions of a breast-like numerical phantom had a deviation in sound speed of 0.14 m/s and a deviation in attenuation of 6.5% from the ground truth. Applications up to now are breast cancer diagnostics and non-destructive testing.