Through-The-Wall Radar Imaging With Wall Clutter Removal Via Riemannian Optimization On The Fixed-Rank Manifold

We introduce a new method for Through-the-Wall Radar Imaging (TWRI) that detects the location of stationary targets hidden by a wall. A crucial step is the mitigation of wall returns which obscure the scene and which are characterized by their low-rankedness given the radar measurement setup. Whereas existing methods make use of nuclear norm minimization or Truncated Singular Value Decomposition (TSVD), we propose to leverage Riemannian optimization over the manifold of fixed-rank matrices in order to use robust estimation while keeping the original rank constraint without relaxation. A detection step via sparse recovery is then performed and the overall method is compared with existing methods over simulated scenes. The results show that the proposed method achieves a better performance.