The detection of multiple targets in an enclosed scene, from its outside, is a challenging topic of research addressed by Through-the-Wall Radar Imaging (TWRI). Traditionally, TWRI methods operate in two steps: first the removal of wall clutter then followed by the recovery of targets positions. Recent approaches manage in parallel the processing of the wall and targets via low rank plus sparse matrix decomposition and obtain better performances. In this paper, we reformulate this precisely via a RPCA-type problem, where the sparse vector appears in a Kronecker product. We extend this approach by adding a robust distance with flexible structure to handle heterogeneous noise and outliers, which may appear in TWRI measurements. The resolution is achieved via the Alternating Direction Method of Multipliers (ADMM) and variable splitting to decouple the constraints. The removal of the front wall is achieved via a closed-form proximal evaluation and the recovery of targets is possible via a tailored Majorization-Minimization (MM) step. The analysis and validation of our method is carried out using Finite-Difference Time-Domain (FDTD) simulated data, which show the advantage of our method in detection performance over complex scenarios.

翻译：从封闭场景外部检测多个目标是一个具有挑战性的研究课题，穿墙雷达成像（TWRI）正是解决此问题的手段。传统TWRI方法分两步进行：首先去除墙体杂波，然后恢复目标位置。近期方法通过低秩加稀疏矩阵分解并行处理墙体与目标，获得了更优性能。本文精确地将此问题重构为RPCA类型，其中稀疏向量以Kronecker积形式出现。我们通过引入具有灵活结构的鲁棒距离来扩展该方法，以处理TWRI测量中可能出现的异质噪声与异常值。采用交替方向乘子法（ADMM）与变量分裂解耦约束实现求解。通过闭式近端估计实现前墙去除，并借助定制的最小化-最大化（MM）步骤恢复目标。利用时域有限差分（FDTD）仿真数据对所提方法进行分析与验证，结果表明在复杂场景下，本方法在检测性能上具有优势。