Phase Error Correction for Approximated Observation-Based Compressed Sensing Radar Imaging

Defocus of the reconstructed image of synthetic aperture radar (SAR) occurs in the presence of the phase error. In this work, a phase error correction method is proposed for compressed sensing (CS) radar imaging based on approximated observation. The proposed method has better image focusing ability with much less memory cost, compared to the conventional approaches, due to the inherent low memory requirement of the approximated observation operator. The one-dimensional (1D) phase error correction for approximated observation-based CS-SAR imaging is first carried out and it can be conveniently applied to the cases of random-frequency waveform and linear frequency modulated (LFM) waveform without any a priori knowledge. The approximated observation operators are obtained by calculating the inverse of Omega-K and chirp scaling algorithms for random-frequency and LFM waveforms, respectively. Furthermore, the 1D phase error model is modified by incorporating a priori knowledge and then a weighted 1D phase error model is proposed, which is capable of correcting two-dimensional (2D) phase error in some cases, where the estimation can be simplified to a 1D problem. Simulation and experimental results validate the effectiveness of the proposed method in the presence of 1D phase error or weighted 1D phase error.