On the Numerical Implementation of the Multiplicative Regularization in Microwave Imaging

We consider the widely-used weighted L
₂
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.