With the advances in radar technology, through-the-wall radar imaging (TWRI) has become a viable sensing modality that can allow fire-and-rescue personnel, police, and military forces to detect, localize, and identify targets behind opaque obstacles. Many of the existing TWRI approaches detect either stationary or moving targets but not both of them simultaneously. In this article, a method is proposed to detect both stationary and moving targets from a sequence of radar signals. The proposed method decomposes the 3-D radar data, i.e., frequency, space, and time data into a low-rank tensor and two sets of sparse images. One set of images comprises the stationary targets, and the other set of images contains the moving targets. Wall clutter removal and target detection are formulated into an optimization problem regularized by tensor low-rank, joint sparsity, and total variation constraints. Then, an alternating direction technique is developed to reconstruct the sets of stationary and moving target images. Experiments using simulated and real radar signals are conducted. The experimental results illustrate the effectiveness of the proposed method to detect and separate the stationary and moving targets into a pair of sparse images.