NUFFT-based fast reconstruction for sparse microwave imaging

Compressive sensing (CS) theory has been applied to sparse microwave imaging in many ways that provide better performance and significantly reduce the sampling rate. However, the computational complexity of reconstruction puts strict constraint on some practical applications with large-scale problems in radar imaging. In this paper, we propose a novel fast reconstruction scheme by realizing the traditional matched filtering with CS technique, which maintains the good performance of matched filtering with a reduced number of observations. Meanwhile, a new sparse basis is formed which offers excellent potential for reducing the computational complexity in reconstruction with fast Fourier transform (FFT) and nonuniform FFT, i.e. NUFFT, where the computational complexity can decrease from O(2MN) to O(4N log N). The feasibility and efficiency of the proposed scheme are validated as well through both numerical simulations and raw data processing results.