Multi-stage compressed sensing and wall clutter mitigation for through-the-wall radar image formation

In this paper, a multi-stage through-the-wall radar imaging technique combining wall clutter mitigation and scene reconstruction is proposed. In the first stage, compressed sensing is applied to compressive measurements to recover the radar signals in the wavelet domain. Then, a subspace projection method is employed to remove the wavelet coefficients associated with the exterior wall reflections. In the second stage, the remaining wavelet coefficients are further compressed using principal component analysis. A compact linear measurement model is then formulated which relates the compressed wavelet coefficients to the image of the scene. Finally, the image reconstruction problem is solved in a more efficient compressed sensing framework, using the compact linear measurement model. Experiment results obtained from real data prove that the proposed method is more efficient and achieves better performance, in terms of target-to-clutter ratio, than direct compressed sensing signal recovery method and delay-and-sum beamforming.