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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 transmitters and receivers. We incorporate a priori information about the multipathing environment, which in our case consists of a fixed reflector. The scene of interest consists of a distribution of moving objects. We base our imaging technique on a modification of the filtered-backprojection method that produces a phase-space image. We characterize the performance of the imaging system by means of its point-spread function, and we analyze the effect of parameters such as sensor positioning and waveforms. We ultimately find that enhanced phase-space resolution can be achieved using multiple sensors and appropriate waveforms.