Generalisation of inverse synthetic aperture radar autofocusing methods based on the minimisation of the Renyi entropy

Resumen

In order to obtain focused inverse synthetic aperture radar (ISAR) images, an accurate translational motion compensation is required. The phase adjustment step corresponds to fine compensation and must be properly designed. The authors introduce the Rényi entropy for autofocusing ISAR images. The Rényi entropy of order α is a generalisation of the standard Shannon entropy. When α tends to be the unity, the Rényi entropy tends to be the Shannon entropy. Here, we demonstrate that minimising the Rényi entropy for α=2 is equivalent to maximising the contrast for ISAR autofocusing. Furthermore, it is also shown that maximising the peak value is equivalent to minimising the Rényi entropy for α tending to infinity. On the other hand, the authors propose to minimise the Rényi entropy with α=0.5 to reconstruct an accurate ISAR image. Simulated data have been used to verify that, in terms of mean squared error, the proposed method with α=0.5 outperforms other autofocusing algorithms such as the method based on contrast maximisation or the one based on the minimisation of the standard Shannon entropy. The method has also been applied to real data.