Inverse problems of layer-by-layer ultrasonic tomography with the data measured on a cylindrical surface

This paper is dedicated to developing efficient methods to solve inverse problems of wave tomography. The proposed new scheme of layer-by-layer tomography of 3D objects uses the experimental data measured on a cylindrical surface. This scheme provides the measurements of both the reflected and the transmitted waves and can easily be implemented in practice. The mathematical model used to solve the inverse problem takes into account the ultrasound diffraction and absorption effects. The authors developed efficient numerical methods to reconstruct the sound speed cross section using the tomographic data measured on the cylindrical surface. These methods are aimed primarily at early breast cancer diagnosis. The inverse problems of ultrasonic tomography are nonlinear and very computationally expensive. The efficiency of the developed methods is illustrated via numerical simulations. The numerical algorithm is implemented on GPU.