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Due to several sources of multipath in through-wall radar sensing, such as walls, floors, and ceilings, there could exist multipath ghosts associated with a few genuine targets in the synthetic aperture beamformed image. The multipath ghosts are false positives and therefore confusable with genuine targets. Here, we develop a multipath exploitation technique using point spread functions, which associate and map back the multipath ghosts to their genuine targets, thereby increasing the effective signal-to-clutter ratio (SCR) at the genuine target locations. To do so, we first develop a multipath model advocating the Householder transformation, which permits modeling multiple reflections at multiple walls, and also allows for unconventional room/building geometries. Second, closed-form solutions of the multipath ghost locations assuming free space propagation are derived. Third, a nonlinear least squares optimization is formulated and initialized with these free space solutions to localize the multipath ghosts in through-wall radar sensing. The exploitation approach is general and does not require a priori assumptions on the number of targets. The free space multipath ghost locations and exploitation technique derived here may be used as is for multipath exploitation in urban canyons via synthetic aperture radar. Analytical expressions quantifying the SCR gain after multipath exploitation are derived. The analysis is validated with experimental EM results using finite-difference time-domain simulations.