An initial frequency-chirp rate spectrum reconstruction framework and its application in SA-ISAR imaging of maneuvering targets

Sparse initial frequency-chirp rate (IFCR) spectrum reconstruction of sparse aperture linear frequency modulation (SA-LFM) signal is crucial in SA inverse synthetic aperture radar (SA-ISAR) imaging for maneuvering targets. To avoid both the reconstruction error introduced by the matched phase-based spectrum and the optimal l₁ regularization coefficient selection, this paper proposes a framework to reconstruct IFCR spectrum of SA-LFM signal. It first constructs the initial IFCR spectrum by the proposed weighted fast iterative shrinkage thresholding (WFISTA) algorithm with a small l₁ regularization coefficient, followed by the band exclude (BE) technique to eliminate the influence of the strong correlation between atoms. Assuming the signal atoms' normalized amplitude is greater than both that of non-signal atom and a preset threshold, the non-signal atoms are iteratively removed into convergence. The IFCR spectrum served as the atom removal criterion is generated by WFISTA, ridge regression under varying coefficient, and the proposed improved local optimization (ILO) technique. The ILO additionally eliminates the BE-generated adjacent atom errors and corrects the spectrum amplitude via least square estimation. Furthermore, based on the strongest azimuth signal's amplitude estimated via the Dechirp algorithm in each range bin, we design a range bin adaptive l₁ regularization coefficient determination principle for the proposed framework and subsequently form the ISAR image. Finally, the experiment results validate the effectiveness of the proposed framework with its application in SA-ISAR imaging.