Airborne Radar Super-Resolution Imaging Based on Fast Total Variation Method

Total variation (TV) is an effective super-resolution method to improve the azimuth resolution and preserve the contour information of the target in airborne radar imaging. However, the computational complexity is very high because of the matrix inversion, reaching $O\left(N^3\right)$. In this paper, a Gohberg–Semencul (GS) representation based fast TV (GSFTV) method is proposed to make up for the shortcoming. The proposed GSFTV method fist utilizes a one-dimensional TV norm as the regular term under regularization framework, which is conducive to achieve super-resolution while preserving the target contour. Then, aiming at the very high computational complexity caused by matrix inversion when minimizing the TV regularization problem, we use the low displacement rank feature of Toeplitz matrix to achieve fast inversion through GS representation. This reduces the computational complexity from $O\left(N^3\right)$ to $O\left(N^2\right)$, benefiting efficiency improvement for airborne radar imaging. Finally, the simulation and real data processing results demonstrate that the proposed GSFTV method can simultaneously improve the resolution and preserve the target contour. Moreover, the very high computational efficiency of the proposed GSFTV method is tested by hardware platform.