Computationally Efficient Sparse Aperture ISAR Autofocusing and Imaging Based on Fast ADMM

In the case of sparse aperture, the coherence between pulses of radar echo is destroyed, which challenges inverse synthetic aperture radar (ISAR) autofocusing and imaging. Mathematically, reconstructing the ISAR image from the sparse aperture radar echo is a linear underdetermined inverse problem, which, by nature, can be solved by the fast developed compressive sensing (CS) or sparse signal recovery theory. However, the CS-based sparse aperture ISAR imaging algorithms are generally computationally heavy, which becomes the bottleneck of preventing their applications to the real-time ISAR imaging system. In this article, we propose a novel and computationally efficient ISAR autofocusing and imaging algorithm for sparse aperture. We first consider a generalized CS model for ISAR imaging and autofocusing with sparse and entropy-minimization regularizations, and then utilize the alternating direction method of multipliers (ADMM) algorithm to optimize the model. To improve computational efficiency, the matrix inversion is translated to an elementwise division with the usage of a partial Fourier dictionary, and the 2-D ISAR image is updated as a whole instead of range cellwise. To achieve autofocusing for sparse aperture, the phase error is estimated by minimizing the entropy of the ISAR image reconstructed in each iterative loop. Experiments based on both simulated and measured data validate that the proposed algorithm can achieve well-focused ISAR images within a few seconds, which is ten times faster than the reported sparse aperture ISAR imaging algorithms.