Compressed sensing for SAR-based wideband three-dimensional microwave imaging system using non-uniform fast fourier transform

A new compressed sensing (CS) image reconstruction method is proposed for high-resolution wideband threedimensional synthetic aperture radar (SAR) imaging systems. In contrast to existing CS SAR methods that employ only a forward SAR transform in pre- or post-processing, the proposed method employs both forward SAR and reverse SAR (R-SAR) transforms in each CS iteration to improve the quality of reconstructed images. This study proposes a simple and elegant truncation repair method to combat the truncation error and utilises non-uniform fast Fourier transform to reduce the SAR and R-SAR transform errors, thereby ensuring the convergence of the CS algorithm and improving the quality of the reconstructed images. The proposed CS SAR method is applied to microwave and millimeter wave imaging systems for non-destructive evaluation of materials embedded in stratified media. Three different specimens under test are measured by conventional uniform sampling and by random under-sampling with 20% or 30% spatial points of the uniform sampling. The reconstructed images show that, albeit having much less measurement points, the proposed CS method achieves better image quality and lower background artefacts than the images reconstructed from the fullysampled uniform measurements.