A Multiplicative Regularized Gauss–Newton Inversion for Shape and Location Reconstruction

A multiplicative regularized Gauss-Newton inversion algorithm is proposed for shape and location reconstruction of homogeneous targets with known permittivities. The data misfit cost functional is regularized with two different multiplicative regularizers. The first regularizer is the weighted -norm total variation which provides an edge-preserving regularization. The second one imposes a priori information about the permittivities of the objects being imaged. Using both synthetically and experimentally collected data sets, we show that the proposed algorithm is robust in reconstructing the shape and location of homogeneous targets.