Tuesday, October 22, 1996
1610 IOE, The Ford Auditorium
Recent investigations in tomographic imaging are based on solving the nonlinear inverse scattering problem, in which a scattering function representing the region of interest (ROI) is reconstructed from the scattered field measured at points outside that region. A promising approach to solving this problem is the so called distorted Born iterative (DBI) method. In the Born approximation methodology, the total field inside the scattering region is assumed equal to the incident field, which is an acceptable assumption for weak scattering. A Born iterative (BI) procedure improves on this zero-th order Born reconstruction by iteratively solving the forward and inverse scattering problems, thus better approximating the total field inside the ROI. Strongly scattering ROI or complex inhomogeneous background can cause the BI method to diverge due to erroneous initial step. The DBI method solves the nonlinear inverse scattering problem by updating the background propagation matrix (or kernel) as well as the total field everywhere in the ROI and at every iteration. 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 BI methods. However, it is sensitive to measurement noise, due to the seepage of noise into the kernel, and to the regularization process of the ill-posed inverse problem. We discuss a modified DBI method which improves the reconstruction quality in three steps: First, we update the kernel only after a regularized smooth BI solution has been obtained. Second, we confine kernel changes to a subset of the pixels which reflect the nature of the scattering media. Finally, we devise a rank reduction regularization scheme which uses kernel and noise dependent, optimally selected rank. Furthermore, we present a multiple frequency MDBI method, which extends the approach to deal with even stronger scattering media. Finally, we discuss an experimental setup which is used to validate the algorithms in a realistic setting.