目的 针对基于压缩感知（CS）的逆合成孔径雷达（ISAR）成像方法的成像质量和应用一直受到目标场景稀疏性好坏和迭代重建耗时长限制的问题，提出一种基于交替方向乘子法网络（ADMMN）的ISAR成像方法。方法 根据交替方向乘子法（ADMM）求解稀疏假设下CS ISAR成像模型时采取的分裂变量的策略，将凸优化迭代求解过程映射到一个多级的深度神经网络，构建出ADMMN。ADMMN通过训练学习欠采样的ISAR测量数据与高质量目标图像之间的映射关系，借此实现ISAR欠采样数据成像。结果 实验采用仿真卫星数据和实测飞机数据，两种数据的采样率分别为25%和10%。实验结果表明，相较于典型的CS ISAR正交匹配追踪（OMP）成像方法和贪婪卡尔曼滤波（GKF）成像方法，ADMMN成像方法能够更准确地重建目标区域散射点，在虚警（FA）、漏检（MD）和相对均方根误差（RRMSE）等成像质量评估指标上均有改善。在卫星数据成像实验中，相比于OMP和GKF，ADMMN在RRMSE指标上分别降低了49.8%和26.5%。在飞机数据成像实验中，相比于OMP和GKF，ADMMN在RRMSE指标上分别降低了68.7%和74.9%。此外，在验证ADMMN先验信息依赖性的实验中，分别采用卫星训练数据和飞机训练数据训练好的两种ADMMN，都能够对10%的飞机目标测量数据成像。结论 融合深度学习和凸优化迭代求解策略的ADMMN ISAR成像方法能够使用非常少的数据获得高质量的成像结果，且成像效率高。

Objective Traditional inverse synthetic aperture radar (ISAR) imaging uses the range-Doppler (RD) method. Compressive sensing (CS)-based ISAR imaging method that appeared in the last decade can obtain imaging results with high image contrast (IC) and minimal sidelobe interference using few undersampled data. However, the imaging quality and application of the CS ISAR imaging method are limited by the performance of the sparse representation of the target scene and the time-consuming iteration reconstruction. An alternating direction method of multipliers network (ADMMN)-based ISAR imaging method is proposed in this study to improve the image reconstruction quality and efficiency of CS ISAR imaging. Method ADMMN is a model-driven deep neural network (MDDNN) constructed by mapping the iterative steps of the alternating direction method of multipliers (ADMM) algorithm into the architecture of MDDNN. This network architecture can be explicitly expressed in terms of polynomials, which facilitate the generation of an accurate imaging network. The convex optimizing iterative solution process is mapped to a multi-level deep neural network (DNN) according to the strategy of splitting variables adopted by the ADMM algorithm to solve a CS ISAR imaging model under sparse assumption and construct the ADMMN. The network consists of four hidden layers, namely, reconstruction layer, transformation dictionary layer, nonlinear transformation layer, and multiplier update layer. The reconstruction layer is used for ISAR image reconstruction, the transformation dictionary layer is used to extract the sparse representation of the ISAR image, the nonlinear transformation layer is used to obtain the nonlinear characteristics of the ISAR image, and the multiplier update layer is used to update the Lagrange multiplier. ADMMN is trained to learn the mapping relationship between undersampled ISAR measurements and high-quality target images to realize ISAR undersampled data imaging. The target image is the well-focused ISAR image obtained by performing the RD algorithm on ISAR echo data matrix, and the measured data are obtained by 2D random down-sampling in range and cross-range dimensions after pulse compression and motion compensation on ISAR echo data. We use two types of metrics to provide a quantitative evaluation of the imaging performance of the proposed imaging method. One type of metrics is the “true-value”-based metrics, and the other is the conventional metrics for evaluating image quality, in which a high-quality image reconstructed is used via a conventional RD method on full data as the “true-value” image. The metrics used in “true-value”-based evaluation are as follows: false alarm (FA), missed detection (MD), and relative root mean square error (RRMSE). FA denotes the number of scatterers that are reconstructed in the image but are not present in the reference image. MD denotes the number of scatterers that are not reconstructed in the newly generated image but are reconstructed in the reference image. RRMSE measures the reconstruction error of the amplitude of the scatterers. The conventional metrics for evaluating the image quality are target-to-clutter ratio, entropy of the image, and IC. Result Simulation satellite data and measured aircraft data are adopted in the experiment. The sampling rates of the two data are 25% and 10%, respectively. Experimental results show that compared with the traditional CS ISAR reconstruction algorithms of orthogonal matching pursuit (OMP) and greedy Kalman filtering (GKF), the ADMMN imaging method can more accurately reconstruct scattering points in the target area, with clearer target contour and fewer false scattering points in the background. The ADMMN imaging method is also better than the OMP and GKF imaging methods in terms of imaging quality evaluation metrics. In simulation satellite data-imaging experiments, compared with OMP and GKF, ADMMN decreases FA by 8.9% and 5%, MD by 61.7% and 59.4%, and RRMSE by 49.8% and 26.5%, respectively. In measured aircraft data-imaging experiments, compared with OMP and GKF, ADMMN decreases FA by 81.1% and 88.9%, MD by 34.3% and 31.6%, and RRMSE by 68.7% and 74.9%, respectively. This study further uses simulation satellite data to train ADMMN and applies the trained ADMMN to the measured aircraft data imaging to verify whether ADMMN strongly depends on prior information, that is, whether training and imaging data are required to be the same type of target data. Satellite and aircraft data are sampled at a rate of 10%. Experimental results show that the ADMMN trained by satellite training data and the ADMMN trained by aircraft training data can image 10% of the aircraft target measurement data; in other words, the wing and fuselage parts of the aircraft can be reconstructed efficiently. Conclusion In this study, a new ADMMN is constructed, and an ISAR imaging method based on ADMMN is proposed. ADMMN utilizes the ability of the ADMM algorithm to solve sparse imaging problems and DNN’s powerful learning ability. After learning, ADMMN can construct the best mapping between undersampled measurement data and high-quality images. Experimental results show that the proposed ISAR imaging method based on ADMMN can obtain good imaging results when using 10% of random undersampled data, and the network training does not depend strongly on the prior information of the same type of target. Compared with the traditional CS reconstruction algorithms of OMP and GKF, the ADMMN imaging method has a more complete target contour and more accurate scatter location reconstruction. In addition, the proposed imaging method has high computational efficiency and can meet the requirements of real-time processing, though it requires a certain number of training samples for pretraining. The next steps to analyze the influence of training data on the imaging network thoroughly and enhance the stability of the method are to simulate the electromagnetic scattering of the main ISAR targets, construct abundant simulation training samples for ADMMN training, and verify the performance of ADMMN with the measured data to optimize the ADMMN.