This paper addresses the problem of indoor scene reconstruction in compressed sensing through-the-wall radar imaging. The proposed method is motivated by two observations that wall reflections reside in a low-rank subspace and the imaged scene tends to be sparse. The task of mitigating the wall reflections and reconstructing an image of the scene behind-the-wall is cast as a joint low-rank and sparsity constrained optimization problem, where a low-rank matrix captures the wall returns and a sparse matrix represents the formed image. An iterative algorithm is developed to estimate the low-rank matrix and the sparse scene vector from a reduced measurement set. Experimental results using real radar data show that the proposed model is very effective at reconstructing the indoor image and removing wall clutter.