This paper addresses the problem of wall clutter mitigation in through-the-wall radar imaging using compressed sensing. In the proposed method, the radar signals are recovered using a joint Bayesian sparse representation, and the estimated coefficients are transformed into a third-order data tensor. Then, higher-order singular value decomposition (HOSVD) is applied to form a multilinear wall subspace. To remove the returns associated with wall clutter, the radar signal is projected onto the complement of the wall subspace. Furthermore, a compact image formation model is developed using principal component analysis (PCA), which yields a smaller dictionary size and reduced noise. Experimental results show that the proposed HOSVD-based method outperforms the standard SVD-based wall clutter mitigation technique.
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