## 1 Introduction  
Synthetic aperture radar (SAR) is a kind of radar system with the features of all-weather, multi-polarization and penetrability, which played a key role in remote sensing, detection and mapping fields in the past decades [1; 2; 3]. There are four common observation modes for SAR: Stripmap, Scan, Inverse and Spotlight [4]. Because the high resolution is conducive to capturing the structure information of the SAR targets, this paper focuses on Spotlight SAR. It is a beamforming-based observation technology, for which the radio beam will always point to the observation scene. The SAR image reconstruction is to acquire the scatter coefficients and to recover spatial distribution of the scatterers from the reflected waves. To obtain a better imaging resolution, a larger aperture will be synthesised by the coherent processing for the motions of targets relative to the antenna, as the pulse compression is usually applied on the range direction. However, in practical applications, traditional SAR imaging methods encounter many problems. Firstly, the receiver needs a higher sampling rate for the wideband waveform because of the Nyquist sampling limit, which leads to a considerable cost for data storing and processing. Secondly, the conventional techniques often suffer from the sidelobe disturbance which may lead to the performance deterioration of reconstruction, such as fuzzy in the SAR target image, etc. Compressed sensing (CS) [5; 6; 7], as a novel theoretical framework appearing in literature recently, can obtain necessary information via sub-Nyquist sampling rate for sparse signal, which can reduce storage requirement and simplify the design of hardware system. That is why CS has attracted greater attention in SAR imaging. In 2001, [PERSON] et al. introduced the sparse constraint into spotlight SAR imaging, and proposed a method to improve the target feature [8]. CS was first applied in super-resolution radar imaging by [PERSON] et al. in 2007, and a new type of radar system was proposed based on sparse reconstruction [9]. In 2009, [PERSON] et al. analyzed the application of sparse reconstruction in ground-penetrating radar imaging, and proposed a sparse imaging algorithm based on \(l_{1}\)-norm minimization [10]. In the next year, a SAR imaging method based on sparse reconstruction theory was introduced by [PERSON] et al. [11], which can achieve a higher reconstruction resolution than the traditional imaging methods. In 2011, the effect of parameter selection of SAR imaging based on regularized sparse reconstruction was studied by [PERSON] et al. [12]. In order to accelerate the speed of SAR imaging algorithm, a sparse regularization technique based on iterative threshold method was proposed by [PERSON] et al. in 2014 [13]. For moving targets, [PERSON] et al. proposed an efficient SAR imaging method in 2015 [14] combining fractional Fourier transform technology with CS framework. However, these studies dealt only with the spatial sparsity of the observation without exploiting the structural characteristics of scatterers in the target scene. In practice, the imaging results show that the scatterers tend to be aggregated together as clumps. The sparse reconstruction schemes have ability to accomplish SAR imaging based on object-level information of scatterers and possess the robustness to noise [15]. In 2016, [PERSON] proposed a CS-based SAR imaging algorithm with structured sparsity constraint, in which a hierarchical Bayesian learning framework was applied [16]. Since hierarchical model is designed, the requirement for model matching of such kind of algorithm is strict, thus the imaging quality may deteriorate once observation data is mismatched with the model. To solve the above problems, we introduce a tensor decomposition algorithm in this paper both to reap the model robustness and to lower resource requirement. The real-world signal is usually multidimensional and structured. In order to deal with such higher-order data processing problem, tensor decomposition is studied widely.