On the Numerical Implementation of the Multiplicative Regularization in
Microwave Imaging
Abstract
We consider the widely-used weighted L2 norm total variation
multiplicative regularizer (MR) for both the Gauss-Newton inversion
(GNI) and contrast source inversion (CSI) algorithms in microwave
imaging (MWI). It is shown that the proper numerical implementation of
the discretized MR operator is important for the GNI algorithm whereas
the CSI algorithm is more robust with respect to different
implementations of this MR. For the GNI algorithm, the MR operator
should be discretized such that high spatial frequency components are
not present in its nullspace, and also the resulting discrete operator
is positive definite.