Motion estimation and imaging of complex scenes with synthetic aperture radar

We study synthetic aperture radar (SAR) imaging and motion estimation of complex scenes consisting of stationary and moving targets. We use the classic SAR setup with a single antenna emitting signals and receiving the echoes from the scene. The known motion estimation methods for SAR work only in simple cases, with one or a few targets in the same motion. We propose to extend the applicability of these methods to complex scenes, by complementing them with a data pre-processing step intended to separate the echoes from the stationary targets and the moving ones. We present two approaches. The first is an iteration designed to subtract the echoes from the stationary targets one by one. This approach first estimates the location of each stationary target from a preliminary image, and then uses the location to define a filter that removes the corresponding target's echo from the data. The second approach is based on the robust principal component analysis (PCA) method. The key observation is that with appropriate pre-processing and windowing, the discrete samples of the stationary target echoes form a low-rank matrix, whereas the samples of a few moving target echoes form a high-rank sparse matrix. The robust PCA method is designed to separate the low rank from the sparse part, and thus can be used for the SAR data separation. We present a brief analysis of the two methods and explain how they can be combined to improve the data separation for extended and complex imaging scenes. We also assess the performance of the methods with extensive numerical simulations.