Compressed sensing techniques have been applied to through-the-wall radar imaging (TWRI) and multipolarization TWRI for fast data acquisition and enhanced target localization. The studies so far in this area have either assumed effective wall clutter removal prior to image formation or performed signal estimation, wall clutter mitigation, and image formation independently. This paper proposes a low-rank and sparse imaging model for jointly addressing the problem of wall clutter mitigation and image formation in multichannel TWRI. The proposed model exploits two important structures of through-wall radar signals: low-rank structure of the wall reflections and jointly-sparse structure among the different polarization images. The task of removing wall clutter and reconstructing multichannel images of the same scene behind-the-wall is formulated as a regularized least squares problem, where low-rank regularization is enforced for the wall components, and joint-sparsity penalty is imposed on channel images. To solve the optimization problem, an iterative algorithm based on the proximal gradient technique is introduced, which simultaneously estimates the wall interferences and yields multichannel images of the indoor targets. Experiments on real and simulated radar data are conducted under full measurements and compressive sensing scenarios. The results show that the proposed model is very effective at removing unwanted wall clutter and enhancing the stationary targets, even under considerable reduction in measurements.

Abstract. We introduce a robust image-formation approach for through-the-wall radar imaging (TWRI). The proposed approach consists of two stages involving compressive sensing (CS) followed by delay-and-sum (DS) beamforming. In the first stage, CS is used to reconstruct a complete set of measurements from a small subset collected with a reduced number of transceivers and frequencies. DS beamforming is then applied to form the image using the reconstructed measurements. To promote sparsity of the CS solution, an overcomplete Gabor dictionary is employed to sparsely represent the imaged scene. The new approach requires far fewer measurement samples than the conventional DS beamforming and CSbased TWRI methods to reconstruct a high-quality image of the scene. Experimental results based on simulated and real data demonstrate the effectiveness and robustness of the proposed two-stage image formation technique, especially when the measurement set is drastically reduced. 1 Introduction Through-the-wall radar imaging (TWRI) is an emerging technology with considerable research interest and important applications in surveillance and reconnaissance for both civilian and military missions. [1][2][3][4][5][6] To deliver high-resolution radar images in both range and crossrange, TWRI systems use wideband signals and large aperture arrays (physical or synthetic). This leads to prolonged data acquisition and high computational complexity because a large number of samples need to be processed. New approaches for TWRI are therefore needed to obtain high-quality images from fewer data samples at a faster speed. To this end, this paper proposes a new approach using compressive sensing (CS) for through-the-wall radar imaging. CS is used here to reconstruct a full measurement set, which is then employed for image formation using delay-and-sum (DS) beamforming.CS enables a sparse signal to be reconstructed using considerably fewer data samples than what is required by the Nyquist-Shannon theorem. [7][8][9] In through-the-wall radar

This paper introduces a joint low-rank and sparsity-based model to address the problem of wall-clutter mitigation in compressed through-the-wall radar imaging. The proposed model is motivated by two observations that wall reflections reside in a low-rank subspace, and target signals tend to be sparse. In the proposed approach, the task of segregating target returns from wall reflections is formulated as a joint low-rank and sparsity constrained optimization problem. Here, the low rank constraint is imposed on the wall component and the sparsity constraint is used to model the target component. An iterative soft thresholding algorithm is developed to estimate a low-rank matrix of wall clutter and a sparse matrix of target reflections from a reduced measurement set. Once the wall and target components are estimated, the target signals are used for scene reconstruction. Experimental evaluation was conducted using real radar data. The results show that the proposed model is very effective at removing wall clutter and reconstructing the image of behind-thewall targets from reduced measurements. ABSTRACTThis paper introduces a joint low-rank and sparsity-based model to address the problem of wall-clutter mitigation in compressed through-the-wall radar imaging. The proposed model is motivated by two observations that wall reflections reside in a low-rank subspace, and target signals tend to be sparse. In the proposed approach, the task of segregating target returns from wall reflections is formulated as a joint low-rank and sparsity constrained optimization problem. Here, the low rank constraint is imposed on the wall component and the sparsity constraint is used to model the target component. An iterative soft thresholding algorithm is developed to estimate a low-rank matrix of wall clutter and a sparse matrix of target reflections from a reduced measurement set. Once the wall and target components are estimated, the target signals are used for scene reconstruction. Experimental evaluation was conducted using real radar data. The results show that the proposed model is very effective at removing wall clutter and reconstructing the image of behind-the-wall targets from reduced measurements.

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