Fast 3-D Imaging Algorithm Based on Unitary Transformation and Real-Valued Sparse Representation for MIMO Array SAR

Multiple-input multiple-output (MIMO) array synthetic aperture radar (SAR) with array antennas distributed along the cross-track direction can obtain 3-D scene information of the surveillance region. However, the cross-track resolution is unacceptable due to the length limitation of the MIMO antenna array. The superresolution algorithms within the framework of compressive sensing (CS) have been introduced to recover the cross-track signal because of its inherent spatial sparsity. The existing sparse recovery algorithms for 3-D SAR are attempted to find the sparse solution in the complex domain directly, which requires a very high computational complexity. To overcome this problem, a new fast 3-D imaging algorithm based on real-valued sparse representation is proposed in this paper. In this new algorithm, unitary transformation can be employed to transform the sparse signal recovery model of uniform/nonuniform MIMO array SAR from the complex domain to the real domain. Thus, a real-valued reweighted l(2,1)-norm minimization model is established. In addition, a modification of the fast iterative shrinkage-thresholding algorithm (FISTA) is used to reconstruct the 3-D image for further improving the computational efficiency. Moreover, the theoretical analysis of computational complexity of the proposed algorithm is derived when compared with an existing complex domain algorithm. Finally, numerical simulations and MIMO array SAR real experimental results are illustrated to validate that the proposed algorithm can reduce the computational complexity significantly in terms of CPU time while still maintaining the inherent advantages of superresolution and robustness against the noise.