Generalised pareto distribution-based Bayesian compressed sensing inverse synthetic aperture radar imaging

The widely used distributions in Bayesian compressed sensing (BCS) inverse synthetic aperture radar (ISAR) imaging do not support stable linear dimensionality reduction, and the compressibility of the recently proposed distributions is hard to be proved theoretically. However, generalised pareto distribution (GPD) can overcome these shortcomings. So a GPD-based ISAR imaging method has been proposed. Interestingly, shape parameter can be set to a small value directly based on mathematical proof in one kind of GPD-Meridian distribution, which is totally different from the existing methods. It not only simplifies the method but also improves the sparsity of the solution. It has been proved that the proposed method now is equal to the log-sum minimisation, which verifies the correctness of the parameter selecting algorithm. Compared with the conventional methods, the new method can recover signals with fewer measurements or in looser sparsity conditions or with smaller recovery errors. When applied into simulated and real ISAR data imaging, the proposed method has obtained better images than the conventional methods. Therefore, the proposed method is a promising imaging method in BCS ISAR imaging.