New classes of reconstruction methods in reflection mode diffraction tomography

Reflection mode diffraction tomography (DT) is an inversion scheme used to reconstruct the spatially variant refractive index distribution of a scattering object. We propose a linear strategy that makes use of the statistically complementary information inherent in the reflected scattered data to achieve a bias-free reduction of the image variance in two dimensional (2D) reflection mode DT. We derive infinite classes of estimation methods that can estimate the 2D Radon transform of the (band-pass filtered) scattering object function from the reflected scattered data. When the insonifying source is broadband we demonstrate that incorporation of the statistically complementary information generated by each frequency in the incident spectrum can further reduce the variance of the images reconstructed using different estimation methods.