Tuesday, October 22, 1996
4:30-5:30 pm
1610 IOE, The Ford Auditorium
Abstract -
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.