Adaptive regularization of a distorted Born iterative algorithm for diffraction tomography

We propose a new approach for solving the nonlinear inverse scattering problem for tomographic imaging based on the distorted Born iterative (DBI) method. The DBI method solves this problem starting with the classical Born approximation, then, at every iteration, it solves the forward and inverse scattering problems utilizing the most recent estimates of the scattering function, the total field in the region of interest (ROI), and the kernel. The DBI method is known to provide good quality reconstructions of regions with higher contrast levels than can be handled by the Born or the Born iterative (BI) methods. However, it is highly sensitive to noise due to noise seepage into the kernel. Our modified DBI algorithm improves the robustness in three steps: First, we update the kernel only after a regularized smooth solution has been obtained. Second, we confine kernel changes to a subset of the pixels in the ROI. Finally, we devise a regularization scheme which uses kernel and noise dependent, optimally selected rank. Such modifications maintain appropriate regularization, thus producing visibly and quantitatively better reconstructions than those obtained by the DBI method.