We consider the problem of synthetic aperture radar (SAR) imaging and motion estimation of complex scenes. By complex we mean scenes with multiple targets, stationary and in motion. We use the usual setup with one moving antenna emitting and receiving signals. We address two challenges: (1) the detection of moving targets in the complex scene and (2) the separation of the echoes from the stationary targets and those from the moving targets. Such separation allows high resolution imaging of the stationary scene and motion estimation with the echoes from the moving targets alone. We show that the robust principal component analysis (PCA) method which decomposes a matrix in two parts, one low rank and one sparse, can be used for motion detection and data separation. The matrix that is decomposed is the pulse and range compressed SAR data indexed by two discrete time variables: the slow time, which parametrizes the location of the antenna, and the fast time, which parametrizes the echoes received between successive emissions from the antenna. We present an analysis of the rank of the data matrix to motivate the use of the robust PCA method. We also show with numerical simulations that successful data separation with robust PCA requires proper data windowing. Results of motion estimation and imaging with the separated data are presented, as well.