Superresolution Downward-Looking Linear Array Three-Dimensional SAR Imaging Based on Two-Dimensional Compressive Sensing

For downward-looking linear array 3-D synthetic aperture radar (SAR), the azimuth and cross-track resolution are unacceptable due to the length limitation of synthetic aperture and linear array. Hence, superresolution reconstruction algorithms are desired. Since the signal to be reconstructed is sparse on the 2-D azimuth-cross-track plane, it is quite suitable to apply the compressive sensing theory to obtain the images. The existed imaging algorithms for downward-looking linear array 3-D SAR are based on 1-D compressive sensing, which could bring the couple effect between different directions. To solve this problem, a novel 3-D imaging algorithm based on 2-D compressive sensing is proposed in this paper. Instead of converting the sparse reconstruction of 2-D matrix signals to the sparse reconstruction of 1-D vectors, the proposed algorithm directly reconstructs the 2-D sparse signals on overcomplete dictionaries with separable atoms. It not only provides superresolution performance, but also reduces the storage of data acquisition and processing. Furthermore, a definition of joint sparse sampling strategy is given to reconstruct the measurement matrices for further improving the computational efficiency of the imaging algorithm. Moreover, in order to investigate the limits of the proposed algorithm, the theory analysis of Cramér-Rao bound is derived and compared with the standard deviation. Finally, numerical simulations under the noise scenarios and the principle prototype experiment on real data are shown to demonstrate the validity and the limits of the proposed algorithm.