Through Wall Radar Imaging aims to see through walls using electromagnetic waves. Low rank and sparse decomposition methods have been effective in processing returns in order to distinguish the wall response from the interior scene. However, they rely on model assumptions that can be a poor approximation of the actual physics. In the meantime, data-driven methods based on Deep Learning can provide an improvement regarding to this limitation. We thus propose a new unrolled network inspired by Robust PCA and Convolutional Sparse Coding which proves to be competitive and especially efficient in scarce data regimes.