Novel approach for a bias-free reduction of image variance in ultrasonic diffraction tomography

In this work, we considered the optimal noise control in image reconstruction in ultrasonic diffraction tomography (UDT). 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 UDT. This strategy leads to the development of an infinite class of hybrid algorithms that reconstruct UDT images from the measured scattered data. We also developed infinite classes of generalized filtered back-propagation (GFBPP) algorithms that include the widely used filtered back-propagation (FBPP) algorithm as a special member. Furthermore, we established the corresponding relationship between the hybrid and GFBPP algorithms. In the absence of noise, these hybrid and GFBPP algorithms are identical. However, they respond to noise and the effect of finite sampling differently. Our simulation studies validate these theoretical results.