Target vibrations introduce nonstationary phase modulation, which is termed the micro-Doppler effect, into returned synthetic aperture radar (SAR) signals. This causes artifacts, or ghost targets, which appear near vibrating targets in reconstructed SAR images. Recently, a vibration estimation method based on the discrete fractional Fourier transform (DFrFT) has been developed. This method is capable of estimating the instantaneous vibration accelerations and vibration frequencies. In this paper, a deghosting method for vibrating targets in SAR images is proposed. For single-component vibrations, this method first exploits the estimation results provided by the DFrFT-based vibration estimation method to reconstruct the instantaneous vibration displacements. A reference signal, whose phase is modulated by the estimated vibration displacements, is then synthesized to compensate for the vibration-induced phase modulation in returned SAR signals before forming the SAR image. The performance of the proposed method with respect to the signal-to-noise and signalto-clutter ratios is analyzed using simulations. Experimental results using the Lynx SAR system show a substantial reduction in ghosting caused by a 1.5-cm 0.8-Hz target vibration in a true SAR image
