Phaseless Gauss-Newton Inversion for Microwave Imaging

Abstract

A phaseless Gauss-Newton inversion (PGNI) algorithm is developed for microwave imaging (MWI) applications. In contrast to full-data MWI inversion that uses complex (magnitude and phase) scattered field data, the proposed PGNI algorithm inverts phaseless (magnitude-only) total field data. This PGNI algorithm is augmented with three different forms of regularization, originally developed for complex GNI. First, we use the standard weighted L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm total variation multiplicative regularizer, which is appropriate when there is no prior information about the object being imaged. We then use two other forms of regularization operators to incorporate prior information about the object being imaged into the PGNI algorithm. The first one, herein referred to as SL-PGNI, incorporates prior information about the expected relative complex permittivity values of the object of interest. The other, referred to as spatial prior PGNI (SP-PGNI), incorporates SPs (structural information) about the objects being imaged. The use of prior information aims to compensate for the lack of total field phase data. The PGNI, SL-PGNI, and SP-PGNI inversion algorithms are then tested against synthetic and experimental phaseless total field data.