Analytical rigid body reconstruction after micro-Doppler removal

Recently, an L-statistics based method for a successful micro-Doppler effects removal and reconstruction of the rigid body in the ISAR/SAR imaging has been proposed. During the procedure of the micro-Doppler removal, a part of the short-time Fourier transform samples that correspond to the rigid body is eliminated, as well. On the other hand, the Fourier transform of a rigid body is reconstructed based on the remaining short-time Fourier transform samples. If all the samples corresponding to the rigid body are unchanged, one highly concentrated peak as in the original Fourier transform would be obtained by this reconstruction. However, due to the removed samples of the short time Fourier transform, a number of undesired low-concentrated components spread around this peak will appear in the reconstructed Fourier transform, as well. In this paper, we propose a procedure for analytical reconstruction of the removed short-time Fourier transform samples that correspond to the rigid body. The proposed procedure leads to a highly concentrated Fourier transform (ISAR/SAR image) obtained by summing over time the resulting short-time Fourier transform filled up with the estimation of the missing rigid body related samples.