Sparse Aperture ISAR Autofocusing and Imaging Algorithm Based on Log-Sum Regularization

Mathematically, the autofocusing and imaging model for sparse aperture inverse synthetic aperture radar (ISAR) has an infinite number of solutions, even with the addition of some sparsity constraints. What relationship exists between these infinite solutions should be answered. In addition, some existing approaches suffer from troublesome manual fine-tuning parameters, or high algorithmic complexity, or low reconstruction accuracy. To deal with the above problems, a sparse aperture ISAR autofocusing and imaging method combining phase estimation and log-sum minimization is proposed in this article, which has high estimation accuracy and computational efficiency, and avoids complicated manual parameter adjustment. Focusing on the model with a phase diagonal matrix and log-sum function, we reveal why there are countless solutions and what relationships exist between them. These features are shared by other models including different regularization functions. Without sparsity prior, the regularization parameter of the algorithm is changed automatically at each iteration according to the ratio of the selected element to the maximum absolute value element in an auxiliary matrix, which controls that only a few elements participate in the computation at each iteration. Coupled with the situation that computationally heavy matrix inversion operations are not required, the calculation speed of the approach is greatly boosted. To show the stability of the algorithm, its convergence is proven without any assumptions. Experiments based on both simulation and measurement data demonstrate that compared with the recently proposed algorithms by others, the proposed algorithm can achieve well-focused ISAR images in less than one second and is very efficient to implement.