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Through-the-wall radar imaging is a sensing technology that can be used by first responders to see through obscure barriers during search-and-rescue missions or deployed by law enforcement and military personnel to maintain situational awareness during tactical operations. However, the strong reflections from the front wall and other obstacles render the detection of stationary targets very difficult. In this article, a learning-based approach is proposed to mitigate the effect of the wall and background clutter. A sparse autoencoder with a low-rank projection is developed to mitigate the wall clutter and recover the target signal. The weights of the proposed autoencoder are determined by solving an augmented Lagrange multiplier optimization problem, and the regularization parameters are estimated using the Bayesian optimization technique. Experiments using real data from a stepped-frequency radar were conducted to illustrate its effectiveness for wall clutter removal. The results show that the proposed method achieves superior performance compared with the existing approaches. [ABSTRACT FROM AUTHOR]