High Resolution ISAR Imaging Algorithm Based on Robust Two-tier Group LASSO Alternating Direction Method of Multipliers

The classical sparse recovery of Inverse Synthetic Aperture Radar (ISAR) imagery obtains the ISAR image by solving the constrained problem of ${\ell _{1}}$ norm regularization. However, this manner may remove the scattering points in low amplitude, and accordingly, lose the structural features in weak scattering. To this end, a novel and Robust Two-tier Group LASSO-Alternating Direction Method of Multipliers (RTGL-ADMM) is proposed in this paper, which is capable of enhancing block sparsity structures of the targets-of-interests. Based on the sparse prior of the target, the proposed algorithm further introduces the prior knowledge of spatial continuity structure of the target’s scatters, and the ${\ell _{1}}/{\ell _{\rm{F}}}$ mixed norm is accordingly used to formulate the prior. Next, the non-smooth ${\ell _{1}}/{\ell _{\rm{F}}}$ mixed norm penalty term is presented under the ADMM framework, where the scatters in both range and azimuthal directions are grouped and overlapped to enhance the block sparsity outer the groups. According to the theory of ADMM, the proximal mapping of the ${\ell _{1}}/{\ell _{\rm{F}}}$ mixed norm is solved and dually iterated to achieve a robust and efficient solution. The proposed algorithm proceeds in the "Decomposition-Coordination" manner, which guarantees superior convergence. In this way, the sparse imaging of ISAR data is combined with the enhancement of structural features. The experiment verifies the adoption of ISAR simulation complex data and YAK-42 measured data, and conducts qualitative analysis against RTGL-ADMM. Then the phase transition curve is used to analyze quantitatively the imaging capability of RTGL-ADMM under different parameters, thus verifying the robustness and superiority of the proposed algorithm in the application of ISAR high-resolution imaging.