This paper presents a system model and inversion for imaging moving targets using phased arrays. The system model provides a mathematical framework to represent the motion of a moving target in the beam-steering domain which is identified as the slow-time domain. The inversion provides a reconstruction of the moving targets in the spatial and velocity domains. It is shown that a randomized beam steering strategy in the slow-time domain can improve the resolution in the velocity domain. The imaging problem is also formulated for a phased array system that spotlights a target area with its transmitted beam to improve the target to clutter power ratio, and obtains beam-steered data in the receive mode for high-resolution imaging. We cite a diagnostic medical ultrasound problem due to the practical difficulties and challenges that are associated with it.
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