Entropy-based motion error correction for high-resolution spotlight SAR imagery

Spotlight synthetic aperture radar (SAR) is an effective way to obtain finer azimuth resolution than the achievement in strip-map mode with the same physical antenna. In general, for spotlight SAR imaging, high azimuth resolution requires long synthetic aperture length. However, in practical airborne applications, because of the inevitable atmospheric turbulence during the long flight trajectory, more complicated motion error is induced that severely degrades the focusing quality of the SAR image. It makes motion compensation (MOCO) for high-resolution spotlight (HR-Spotlight) SAR imagery more difficult than that for other SAR systems. To tackle the HR-Spotlight SAR data contaminated by the complicated motion error, a novel MOCO algorithm based on entropy minimisation is proposed, which is named by minimum entropy MOCO (ME-MOCO). In this approach, by fitting a polynomial to the motion error, the entropy of a focused image is utilised as the optimisation function of the polynomial coefficients. Attributed to damped Newton method, a modified strategy is designed, which results in that the data-driven ME-MOCO algorithm estimates high order polynomial parameters accurately and efficiently. Besides, the proposed algorithm is efficient for the capability of exploiting the fast Fourier transform through the processing chain. Real data experiments and comparisons demonstrate the effectiveness and superiority of the proposal.