Sparse ISAR Imaging Algorithm Based on Bayesian-Lasso

Due to the echoes of the Inverse Synthetic Aperture Radar (ISAR) imagery are spatially sparse, the conventional convex optimization for the sparse image recovery involves tedious adjustment for the regularization parameter, which seriously limits the accuracy and the convenience of the image formation. In this paper, the unconstrained least absolute shrinkage and selection operator (Lasso) model is introduced for the $ {\ell _1}$ regularization problem, and it is equivalently transformed into sparse Bayesian inference under the Laplacian prior. More specifically, a hierarchical Bayesian model is established. In such cases, multiple hyper-parameters with multi-level conditional probability distribution are introduced. Due to the equivalent transformation, the manual choice of the regularization parameter can be replaced by automatic determination under the hierarchical Bayesian model, which provides convenience of fully conditional probability adjustment. Considering the high dimensions of sparse image responses and multiple hyper-parameters, the Gibbs sampler is adopted, where the Bayesian posterior of the ISAR image and high-dimensional hyper-parameters can be solved with fully confidence. Based on the research in this paper, all parameters can be attained by data, therefore tedious parameter adjustment can be avoided, and the automation level of the algorithm can be improved. The effectiveness and superiority of this method are proved by both simulated and measured data experiments.