Imaging with waves bounced from a dispersive reflector

We develop a linearized imaging theory that combines the spatial, temporal, and spectral components of multiply scattered waves. We consider the case of multiple fixed sensors viewing a distribution of multiple moving objects (targets) in an environment in which known multipath scattering takes place. In this paper, we investigate the case in which the multipath scattering is also dispersive, i.e., is different for different frequencies. The strategy is to develop a model for the data that includes the sensor positions, transmitted waveforms, and angle-of-departure of the transmitted field. We use this model to develop an imaging method that is a modification of a tomographic, filtered backprojection method that produces a phase-space image. In this work we also analyze the image via a multidimensional point-spread function and we identify how the imaging system reacts to parameters such as frequency, number of sensors, and wave path. We demonstrate, through example, that enhanced phase-space resolution for a distribution of stationary targets, in the presence of a dispersive reflector, may be achieved via a tomographic approach with a priori knowledge about the wave path and the nature of the multipath scattering.