Fast ISAR Cross-Range Scaling Using Modified Newton Method

Abstract

This paper proposes a fast and novel cross-range scaling algorithm for inverse synthetic aperture radar (ISAR) imaging. The rotational motion of the target unavoidably results in high-order phase errors that blur the ISAR image. To achieve the cross-range scaling and compensate the quadratic phase error, the rotational velocity and rotational center of the target are jointly estimated by optimizing the ISAR image quality in terms of either entropy or contrast. Since it is a two-dimensional nonlinear optimization problem, the grid search is generally computationally inefficient and inaccurate. To improve the computational efficiency, a modified Newton method is introduced by adjusting the Hessian to be positively definite to ensure the iterative optimization process in a correct direction. The proposed algorithm offers the following desirable advantageous features. First, it automatically compensates the quadratic phase errors jointly with the scaling process to improve the image quality. Second, it is a data-driven, rather than image-driven, process that does not depend on the quality of ISAR image. It also performs satisfactorily for the sparse aperture data, while most other algorithms are invalid. The modified Newton method ensures fast convergence. For example, our numerical experiments achieve a precision of $ \bf {10^{-6}}$ with less than ten iterations. Last but not least, the proposed algorithm is robust to noise because our experiments show that it is still effective when signal-to-noise ratio is as low as $-$ 10 dB.