A comparative study of compressed sensing approaches for 3-D synthetic aperture radar image reconstruction

This paper investigates two compressed sensing (CS) approaches that can be used to reconstruct 3-D synthetic aperture radar (SAR) images with undersampled measurements. Combining CS with the range migration algorithm (RMA), using either Stolt transform or non-uniform fast Fourier transform (NUFFT), yields two different approaches: Stolt-CS and NUFFT-CS. These approaches can decrease the load of data acquisition while recovering satisfactory 3-D SAR images through l1-norm optimization. A simulated image is used as the ground truth to facilitate the comparative study. The 2-D structured similarity (SSIM) index is extended to 3-D to assess the quality of the reconstructed images. Both the simulation and the experimental reconstruction results demonstrate that the Stolt-CS contributes little to image quality improvement or computational complexity reduction due to the inaccuracy of the Stolt transform. In contrast, the NUFFT-CS achieves a good tradeoff between the reconstruction quality and the computational costs.