High resolution and wide swath, which are related to imaging quality and observation efficiency, are the key specifications for spaceborne synthetic aperture radar (SAR). Owing to the restrictions of the Nyquist sampling theorem, it is difficult to improve both specifications simultaneously. The increase of the swath width often leads to the decrease of the spatial resolution, e.g., in scanning SAR (ScanSAR) and terrain observation with progressive scan SAR (TOPSAR). For a sparse scene, an image containing only a few targets has massive data but little useful information. This paper proposes a novel SAR observation mode, AgileSAR, which is based on the time-space sampling method and can overcome the limitations of the Nyquist theorem. It also increases the swath width while preserving the resolution of the sparse scene. AgileSAR steers the antenna beam towards a different sub-swath, generally after one or two pulse intervals, and the average pulse repetition rate corresponding to every sub-swath is much lower than that determined by the Nyquist theorem. Compared with Sentinel-1, which can achieve 5-m resolution and 80-km swath, a single azimuth-channel AgileSAR system can achieve 5-m resolution and 300-km swath for a sparse scene, once the corresponding system parameters are designed. The l1 relaxation method is used to reconstruct sparse SAR images, and the reconstruction performance is quantitatively analysed based on the estimation error. Simulation results validating the proposed method with sub-Nyquist samples can achieve approximately similar performance as conventional SAR with Nyquist samples.

Sub-Nyquist sampling technology can ease the conflict between high resolution and wide swath in a synthetic aperture radar (SAR) system. However, the existing sub-Nyquist SAR imposes a constraint on the type of the observed scene and can only reconstruct the scene with small sparsity (i.e., number of significant coefficients). The information channel model of microwave imaging radar based on information theory, in which scene, echo, and the mapping relation between the two correspond to information source, sink, and channel, is built, and noisy-channel coding theorem explains the reason for the aforementioned under this model. To allow the wider application of sub-Nyquist SAR, this paper proposes sub-Nyquist SAR based on pseudo-random space-time modulation. This modulation is the spatial and temporal phase modulation to the traditional SAR raw data and can increase the mutual information of information source and sink so that the scenes with large sparsity can be reconstructed. Simulations of scenes with different sparsity, e.g., an ocean with several ships and urban scenes, were run to verify the validity of our proposed method, and the results show that the scenes with large sparsity can be successfully reconstructed.

Ultra-wide swath synthetic aperture radar (SAR) systems are of great significance for applications such as terrain measurement and ocean monitoring. In conventional SAR systems, targets echo from the near-range and far-range of an observed swath mutually overlap, and the blind ranges are caused by those that the radar cannot receive while it is transmitting. Therefore, the swath of conventional SAR systems is limited due to their range ambiguity as well as the transmitted pulse blockage. With the development of waveform diversity, range ambiguity can be suppressed by radar waveform design with a low-range sidelobe without increasing the system’s complexity when compared to the scan-on-receive (SCORE) based on digital beamforming (DBF) technique. Additionally, by optimizing the pulse repetition interval (PRI) variation strategy, the negative impact of blind range on imaging can be reduced. Based on these technologies, this paper proposes a theoretical architecture to achieve an ultra-wide swath SAR imaging system via chaotic frequency modulation (FM) signals and a random pulse repetition interval variation strategy without increasing the antenna area. By transmitting time-variant chaotic-FM signals, the interference between targets in the near range and far range can be reduced by the corresponding match filters. Furthermore, random pulse repetition intervals increase the irregularity and aperiodicity of the blind ranges to further improve the imaging quality. Simulation results demonstrate that the proposed wide-swath SAR system has better performance compared to classical SAR systems.

Since compressed sensing (CS) theory broke through the limitation of the traditional Nyquist sampling theory, it has attracted extensive attention in the field of microwave imaging. However, conventional CS-based imaging models always suffer from the limitation of sparse properties of the scene itself. In this article, a novel change imaging in the transforming domain based on CS is proposed, which converts the recovery of the scene itself to that of scene change from the historical observation to the current observation. Firstly, a new complex-data sparse microwave imaging model in the transforming domain is built by the real-imaginary separated operation. Then a scene transform method named inverse-whitening processing is introduced to confirm the relationship between the real part, imaginary part, and amplitude part of a complex scene, and the sparse transforming domain is constructed based on this processing and historical observation. At last, a CS algorithm is used to recover this change with undersampling echo, and the scene of the current observation can be achieved by integrating the recovered change with the historical observation. The effectiveness of change imaging in the transforming domain is verified on both simulated and real SAR images.

A novel compressive sensing (CS) synthetic-aperture radar (SAR) called AgileSAR has been proposed to increase swath width for sparse scenes while preserving azimuthal resolution. AgileSAR overcomes the limitation of the Nyquist sampling theorem so that it has a small amount of data and low system complexity. However, traditional CS optimization-based algorithms suffer from manual tuning and pre-definition of optimization parameters, and they generally involve high time and computational complexity for AgileSAR imaging. To address these issues, a pseudo-${\mathcal{L}}_0$-norm fast iterative shrinkage algorithm network (pseudo-${\mathcal{L}}_0$-norm FISTA-net) is proposed for AgileSAR imaging via the deep unfolding network in this paper. Firstly, a pseudo-${\mathcal{L}}_0$-norm regularization model is built by taking an approximately fair penalization rule based on Bayesian estimation. Then, we unfold the operation process of FISTA into a data-driven deep network to solve the pseudo-${\mathcal{L}}_0$-norm regularization model. The network’s parameters are automatically learned, and the learned network significantly increases imaging speed, so that it can improve the accuracy and efficiency of AgileSAR imaging. In addition, the nonlinearly sparsifying transform can learn more target details than the traditional sparsifying transform. Finally, the simulated and data experiments demonstrate the superiority and efficiency of the pseudo-${\mathcal{L}}_0$-norm FISTA-net for AgileSAR imaging.

Sub-Nyquist synthetic aperture radar (SAR) based on pseudo-random time–space modulation has been proposed to increase the swath width while preserving the azimuthal resolution. Due to the sub-Nyquist sampling, the scene can be recovered by an optimization-based algorithm. However, these methods suffer from some issues, e.g., manually tuning difficulty and the pre-definition of optimization parameters, and a low signal–noise ratio (SNR) resistance. To address these issues, a reweighted optimization algorithm, named pseudo-ℒ₀-norm optimization algorithm, is proposed for the sub-Nyquist SAR system in this paper. A modified regularization model is first built by applying the scene prior information to nearly acquire the number of nonzero elements based on Bayesian estimation, and then this model is solved by the Cauchy–Newton method. Additionally, an error correction method combined with our proposed pseudo-ℒ₀-norm optimization algorithm is also present to eliminate defocusing in the motion-induced model. Finally, experiments with simulated signals and strip-map TerraSAR-X images are carried out to demonstrate the effectiveness and superiority of our proposed algorithm.