Through-the-wall radar imaging utilizes electromagnetic wave propagation to reveal the locations and velocities of obscured targets. For a pulsed radar operation, conventional Doppler processing can only estimate the radial velocity component of the indoor moving targets. We show that multipath propagation provides additional Doppler information that allows estimation of the full target velocity vector. We propose a computationally efficient two-step approach that obtains the target locations using sparse reconstruction and estimates the velocities by utilizing the Doppler information in the various propagation paths. We support our findings by simulation and experimental results.