  Through-wall synthetic aperture radar (SAR) imaging is of significant
interest for security purposes, in particular when using multi-static SAR
systems consisting of multiple distributed radar transmitters and receivers to
improve resolution and the ability to recognise objects. Yet there is a
significant challenge in forming focused, useful images due to multiple
scattering effects through walls, whereas standard SAR imaging has an inherent
single scattering assumption. This may be exacerbated with multi-static
collections, since different scattering events will be observed from each angle
and the data may not coherently combine well in a naive manner. To overcome
this, we propose an image formation method which resolves full-wave effects
through an approximately known wall or other arbitrary obstacle, which itself
has some unknown "nuisance" parameters that are determined as part of the
reconstruction to provide well focused images. The method is more flexible and
realistic than existing methods which treat a single wall as a flat layered
medium, whilst being significantly computationally cheaper than full-wave
methods, strongly motivated by practical considerations for through-wall SAR.
