Noise properties of reconstructed images in ultrasonic diffraction tomography

In ultrasonic diffraction tomography, ultrasonic waves are used to probe the object of interest at various angles. The incident waves scatter when encountering inhomogeneities, and thus do not travel in straight lines through the imaged object. When the scattering inhomogeneities are considered weak, the scattering object can be reconstructed by algorithms developed from a generalized central slice theorem. In this work, the authors develop a hybrid algorithm for reconstruction of a scattering object by transforming the measured scattered data into a conventional X-ray-like sinogram thus allowing standard X-ray reconstruction algorithms, such as filtered back-projection, to be applied. The authors systematically investigate and compare the statistical properties of three different algorithms: a direct Fourier inversion algorithm, the filtered back-propagation algorithm (which is analogous to the conventional filtered back-projection algorithm), and the newly developed hybrid algorithm. The authors derive analytical expressions for the variance of the noise in the reconstructed images and investigate the noise properties of the algorithms by performing extensive numerical simulations