Autofocusing for Sparse Aperture ISAR Imaging Based on Joint Constraint of Sparsity and Minimum Entropy

Sparsity and Shannon entropy have been widely used in inverse synthetic aperture radar (ISAR) imaging. The minimum entropy criterion is usually applied in the translational motion compensation and the sparse constraint is used in the azimuth imaging. In this paper, we combine these two criteria to develop a novel autofocusing algorithm for sparse aperture ISAR (SA-ISAR) imaging. First, the Laplace approximation-based variational Bayesian inference with the Laplacian scale mixture prior is proposed for SA-ISAR imaging. Then, the autofocusing is accomplished by minimizing the image entropy of the radar image reconstructed within the sparse Bayesian framework. During the iterations, the sparse constraint and the minimum entropy criteria are interactively used to improve the convergence speed and the robustness to noise. Additionally, the proposed autofocusing algorithm is adaptive and does not need to specifically initialize the phase error with other autofocusing approaches. Experimental results, based on both simulated and measured data, validate that the proposed algorithm can even obtain a well-focused image with SA data containing only 12.5% randomly sampled pulses.