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

In order to obtain focused inverse synthetic aperture radar (ISAR) images, an accurate translational motion compensation is required. The phase adjustment step corresponds to. ne compensation and must be properly designed. The authors introduce the Renyi entropy for autofocusing ISAR images. The Renyi entropy of order alpha is a generalisation of the standard Shannon entropy. When alpha tends to be the unity, the Renyi entropy tends to be the Shannon entropy. Here, we demonstrate that minimising the Renyi entropy for alpha = 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 Renyi entropy for alpha tending to infinity. On the other hand, the authors propose to minimise the Renyi entropy with alpha = 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 alpha = 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.