Noise propagation in diffraction tomography: Comparison of conventional algorithms with a new reconstruction algorithm

In ultrasonic diffraction tomography, ultrasonic waves are used to probe the object of interest at various angles. The incident waves scatter when encountering inhomogeneities, unlike conventional X-ray CT. Theoretically, when the scattering inhomogeneities are considered weak, the scattering object can be reconstructed by algorithms developed from a generalized central slice theorem. We develop a hybrid algorithm for reconstruction of a scattering object by transforming the scattered data into a conventional X-ray-like sinogram thus allowing, standard X-ray reconstruction algorithms, such as filtered back-projection, to be applied. We investigate the statistical properties of the filtered back-propagation, direct Fourier, and newly proposed hybrid reconstruction algorithms by performing analytical as well as numerical studies.