Non-Sparse SAR Imaging From Quadrature Compressive Measurements Based on Magnitude-Phase Separation

Sub-Nyquist synthetic aperture radar (SAR) can recover images from sub-Nyquist samples with a prerequisite that SAR imaging scenes are sparse in certain basis. However, plenty of SAR images are difficult to be sparsely represented, like an extended SAR image with the speckle effect, which leads the sub-Nyquist SAR imaging performance significantly degraded. To solve this problem, this article provides a quadrature compressive sampling (QuadCS) SAR imaging method for non-sparse scenes. Based on the principle of magnitude-phase separation, we can reconstruct the non-sparse SAR image from sub-Nyquist measurements by alternatively resolving its magnitude and phase recovery. The magnitude recovery is coined as a standard sparse reconstruction problem since magnitude images are always sparse in some basis, while the phase recovery is nonlinear least squares which is easily solved by a matched filtering-based method. To achieve fast magnitude recovery, we adopt the fast iterative shrinkage-thresholding algorithm and speed up the matrix-vector products, which consumes the main computational cost, based on the special structure of employed QuadCS system. Furthermore, we provide an independent measurement strategy to inject more randomness into the equivalent QuadCS sensing matrix. Theoretical analysis shows that this strategy makes the sensing matrix have better restricted isometry property, and therefore guarantees that the magnitude recovery requires lower sampling rate or has better performance. Real-data experiment results verify that the proposed SAR imaging method can effectively recover the non-sparse SAR images from sub-Nyquist samples.