Blind Multi-path Elimination by Sparse Inversion in Through-the-Wall-Imaging

In this paper, we propose a multi-path elimination by sparse inversion (MESI) algorithm that removes the clutter induced by internal wall reflections in a Through-the-Wall-Imaging (TWI) system without prior knowledge of the scene geometry. Our approach iteratively recovers the time-domain primary impulse responses of targets behind the front wall then finds a delay convolution operator that best maps the primary impulse response of each target to the multi-path reflections available in the received signal. Since the number of targets and the number of reflecting surfaces is typically much smaller than the downrange extent of the scene, we employ `1 regularized sparse recovery in both the target detection and reflection operator estimation. Moreover, we specify extensions of the MESI algorithm that allow for the detection of targets directly in the image domain even from randomly sub-sampled arrays and compensate for the distortion of the source waveform due to the front wall propagation. We present numerical simulations that demonstrate the effectiveness of MESI in locating targets inside a room with unknown dimensions or wall parameters and highlight the robustness of our scheme to severe measurement noise.