Reinterpretation and Enhancement of Signal-Subspace-Based Imaging Methods for Extended Scatterers

Interior sampling and exterior sampling (or enclosure) signal-subspace-based imaging methodologies for extended scatterers derived in previous work are reformulated and reinterpreted in terms of the concepts of angles and distances between subspaces. The insight gained from this reformulation renders a broader, more encompassing inversion methodology based on a (pseudo) cross-coherence matrix associated to the singular vectors of the scattering or response matrix and the singular vectors intrinsic to a given, hypothesized support region for the scatterers (under a known background Green’s function associated to a known embedding medium where the scatterers reside). A number of new imaging functionals based on that cross-coherence matrix are proposed and numerically shown to perform well in both imaging and shape reconstruction problems. The proposed approaches do not require for their implementation the estimation of a cutoff in the singular value spectrum separating signal from noise subspaces, which is a common computational difficulty in signal subspace methods. In the shape reconstruction context it is also shown how to combine the signal subspace approach with the level set method.