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Three-dimensional (3-D) radar imaging can provide additional information along elevation dimension about the target with respect to the conventional 2-D radar imaging, but usually requires a huge amount of data collected over 3-D frequency-azimuth-elevation space, which motivates us to perform 3-D imaging by using sparsely sampled data. Traditional compressive sensing (CS) based 3-D imaging methods with sparse data convert the 3-D data into a long vector, and then complete the sensing and recovery steps. This 1-D vectorized model, however, faces challenges of high computational complexity and huge memory usage and may not be viable in real applications. In this article, we solve the 3-D sparse imaging problem efficiently in a tensor way. For this aim, we firstly derive the 3-D imaging model from a tensor perspective under some assumptions. Then we review three kinds of sparse data sampling schemes that are common on the existing 3-D compressive radar imaging applications. Subsequently, with the help of prior information hidden in the radar signal, i.e., sparsity and low-rank property, we propose efficient image reconstruction algorithms for different sampling schemes to produce 3-D images with sidelobes and artifacts suppressed significantly. Finally, extensive experiments based on simulated and real-measured datasets are carried out. Results show that the proposed methods can effectively generate competitive images with small reconstruction error even when the data sampling ratio is low, which confirm the validity of proposed methods.
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