Investigation of the noise properties of a new class of reconstruction methods in diffraction tomography

In diffraction tomography (DT), the measured scattered data are unavoidably contaminated by noise. Because the detectability of an object in a noisy image relies strongly on the signal-to-noise ratio, it is important in certain applications to reduce the statistical variation in the reconstructed image. Recently, we revealed the existence of statistically complementary information inherent in the scattered data and proposed a linear strategy that makes use of this information to achieve a bias-free reduction of the image variance in two-dimensional (2D) DT. This strategy leads to the development of an infinite class of estimation methods, that from the measured scattered data, can estimate the Radon transform of the scattering object function. From the estimated Radon transforms, one can readily reconstruct the object function by using a variety of existing reconstruction algorithms. The estimation methods in the class are mathematically equivalent, but they respond to noise differently. We investigated the noise properties of these estimation methods by use of computer simulation studies. The results of our simulation studies demonstrate quantitatively that it is possible to achieve a bias-free variance reduction in the reconstructed scattering object by utilizing complementary statistical information that is inherent in the scattered data.