ISAR autofocus based on sparsity-driven estimation of translational and rotational motion components

Inverse Synthetic Aperture Radar (ISAR) relies on the motion of the observed target to synthetically generate an image. While the motion of the target might be known for controlled turn-table experiments, this is not true for the general case of non-cooperative objects. For The purpose of obtaining a focused high resolution image of the object, the relative motion between the radar and the object must be estimated. The process of estimating the relative motion components based on the received signals only and then compensating them to produce the ISAR image is called ISAR Autofocus. Compressed Sensing (CS) tackles the problem of recovering an unknown signal from fewer measurements than that required by the Shannon's theory. CS assumes that the signal to be recovered is sparse either directly or under some other representation basis. In general, the object's reflectivity distribution is not sparse. However, in some cases, the ISAR measurements can be approximated by the superposition of the echoes of a group of scattering centers. This interpretation of ISAR images allows for the use of CS algorithms for the reconstruction of ISAR images. In this paper, we propose a Compressed Sensing (CS) based algorithm for estimating the relative motion between the radar and the object as a first step for focusing ISAR images. We verify, with simulated data, the ability of the proposed algorithm to estimate both the relative translational and rotational motion of the observed object with respect to the radar. Future work will test the performance of the algorithm with real data as well as modify the algorithm to work with three dimensional motion components.