Passive imaging using distributed apertures in multiple-scattering environments

Abstract

We develop a new passive image formation method capable of exploiting information about multiple scattering in the environment, as well as statistics of the objects to be imaged, additive noise and clutter, using measurements from a sparse array of receivers that rely on illumination sources of opportunity. The array of receivers can be distributed spatially in an arbitrary fashion with several hundred wavelengths apart. We use a physics-based approach to model a multiple-scattering environment and develop a statistical model that relates measurements in a given receiver to measurements in other receivers. The model is based on back-propagating measurements in a given receiver to a hypothetical target location and then forward propagating to another receiver location based on the Green's function of the background environment. We next address the imaging problem as a generalized likelihood ratio test (GLRT) for an unknown target location. The GLRT framework allows a priori scene, clutter and noise information to be incorporated into the problem formulation, as well as non-Gaussian data likelihood and a priori models. We address the spatially resolved hypothesis testing problem by constraining the associated discriminant functional to be linear and by maximizing the signal-to-noise ratio of the test statistics. We use the resulting spatially resolved test statistic to form the image. We present the resolution analysis of our imaging algorithms for free-space and a multiple-scattering environment model. Our analysis demonstrates the improvements in the point spread function and the signal-to-noise ratio of the reconstructed images when multiple scattering is exploited, as well as the potential artifacts and limitations. We present numerical experiments to demonstrate the performance of the resulting algorithms and to validate the theoretical findings.