Through-the-wall radar (TWR) imaging is an emerging technology that enables detection and localization of targets behind walls. In practical operations, TWR sensing faces several technical difficulties including strong wall clutter and missing data measurements. This paper proposes a sparse Bayesian learning (SBL) approach for wall-clutter mitigation and scene reconstruction from compressed data measurements. In the proposed approach, SBL is used to model both the intraantenna signal sparsity and interantenna signal correlation for estimating the antenna signals jointly. Here, the Bayesian framework provides a learning paradigm for sharing measurements among spatial positions, leading to accurate and stable antenna signal estimation. Furthermore, the task of wall-clutter mitigation is formulated as a probabilistic inference problem, where the wall-clutter subspace and its dimension are learned automatically using the mechanism of automatic relevant determination. Automatic discrimination between targets and clutter allows an effective target image formation, which is performed using Bayesian approximation. Experimental results with both real and simulated TWR data demonstrate the effectiveness of the SBL approach in indoor target detection and localization.