Through-the-wall radar imaging (TWRI) is an ongoing field of research which aims at investigating the inside of a building from its outside. In the most common setting, it seeks to detect or monitor stationary targets. Departing from usual delay-and-sum techniques, sparse recovery problems have been proposed to solve this detection problem. These methods rely on a preprocessing step where an appropriate separation of wall and target subspaces is first performed to remove the front wall response. In this work, we explore one-step methods using joint low-rank and sparse decomposition methods through the Robust PCA (RPCA) framework. The novelty is a one-step recovery from a structured inversion problem for which we tailor an Alternating Direction Method of Multipliers (ADMM) algorithm. We validate and compare our method on simulations.