3D mmW sparse imaging via complex-valued composite penalty function within collaborative multitasking framework

Abstract

The emerging three-dimensional (3D) millimeter-wave (mmW) array SAR imaging with compressed sensing (CS) has shown impressive potential for improving image quality. However, the widely used $L_1$ penalty function belongs to convex operators, which introduce bias effects in imaging and reduce reconstruction accuracy. In the context of 3D imaging, a single $L_1$ is inadequate for characterizing the spatial features of the target, resulting in the loss of information. Additionally, the complex-valued nature of SAR data should be considered to further improve imaging performance. Therefore, in this article, a 3D sparse imaging method based on the complex-valued composite penalty function (CCPF) is proposed. Firstly, a CCPF is presented, which combines complex-valued minimax convex penalty (CMCP) and complex-valued 3D total variation (C3DTV) to alleviate bias effects while preserving the spatial structure information of the target. Secondly, the improved collaborative multitasking framework based on variable splitting and alternating minimization is presented to solve optimization problems with CCPF. Furthermore, the proposed method takes into account the complex-valued characteristics of SAR data and preserves the phase information of the imaging scene, which is beneficial for subsequent image interpretation. Finally, the effectiveness of the proposed method has been validated by a substantial amount of experimental data.