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The detection of multiple targets in an enclosed scene, from its outside, isa challenging topic of research addressed by Through-the-Wall Radar Imaging(TWRI). Traditionally, TWRI methods operate in two steps: first the removal ofwall clutter then followed by the recovery of targets positions. Recentapproaches manage in parallel the processing of the wall and targets via lowrank plus sparse matrix decomposition and obtain better performances. In thispaper, we reformulate this precisely via a RPCA-type problem, where the sparsevector appears in a Kronecker product. We extend this approach by adding arobust distance with flexible structure to handle heterogeneous noise andoutliers, which may appear in TWRI measurements. The resolution is achieved viathe Alternating Direction Method of Multipliers (ADMM) and variable splittingto decouple the constraints. The removal of the front wall is achieved via aclosed-form proximal evaluation and the recovery of targets is possible via atailored Majorization-Minimization (MM) step. The analysis and validation ofour method is carried out using Finite-Difference Time-Domain (FDTD) simulateddata, which show the advantage of our method in detection performance overcomplex scenarios.

Through the Wall Radar Imaging via Kronecker-structured Huber-type RPCA