Terahertz SAR Vibration Compensation Based on Alternating Direction Method of Multipliers

Due to the high-frequency and short wavelength of the terahertz wave, airborne terahertz SAR (THz-SAR) can achieve high imaging resolution, but it is sensitive to high-frequency vibration of the platform. In order to bring the image into focus, it is necessary to compensate for the high-frequency vibration error. Different from the methods that approximate the vibration as a sum of several simple harmonic vibrations, this paper proposes a high-frequency error compensation method based on alternating direction method of multipliers (ADMM) without modeling of the vibration, which is effective when the vibration is complex. Firstly, the coarsely focused image is obtained by the azimuth Fourier transform (FFT) to the echo signal, and the vibration compensation can be transformed into minimizing the l1-norm of the image. Then, auxiliary variables are introduced to construct the objective function conforming to the requirements of ADMM. In the process of iteration, an additional step is added to update the phase error by minimizing the image entropy. Finally, the estimated phase error is used for vibration compensation and imaging. The simulation results of point target and distributed imaging scene verify the effectiveness of the proposed method, and the image can be well-focused when the signal-to-noise ratio is low.