Factorized Geometrical Autofocus for Synthetic Aperture Radar Processing

Abstract: Synthetic Aperture Radar (SAR) imagery is a very useful resource for the civilian remote sensing community and for the military. This however presumes that images are focused. There are several possible sources for defocusing effects. For airborne SAR, motion measurement errors is the main cause. A defocused image may be compensated by way of autofocus, estimating and correcting erroneous phase components. Standard autofocus strategies are implemented as a separate stage after the image formation (stand-alone autofocus), neglecting the geometrical aspect. In addition, phase errors are usually assumed to be space invariant and confined to one dimension. The call for relaxed requirements on inertial measurement systems contradicts these criteria, as it may introduce space variant phase errors in two dimensions, i.e. residual space variant Range Cell Migration (RCM). This has motivated the development of a new autofocus approach. The technique, termed the Factorized Geometrical Autofocus (FGA) algorithm, is in principle a Fast Factorized Back-Projection (FFBP) realization with a number of adjustable (geometry) parameters for each factorization step. By altering the aperture in the time domain, it is possible to correct an arbitrary, inaccurate geometry. This in turn indicates that the FGA algorithm has the capacity to compensate for residual space variant RCM. In appended papers the performance of the algorithm is demonstrated for geometrically constrained autofocus problems. Results for simulated and real (Coherent All RAdio BAnd System II (CARABAS II)) Ultra WideBand (UWB) data sets are presented. Resolution and Peak to SideLobe Ratio (PSLR) values for (point/point-like) targets in FGA and reference images are similar within a few percents and tenths of a dB. As an example: the resolution of a trihedral reflector in a reference image and in an FGA image respectively, was measured to approximately 3.36 m/3.44 m in azimuth, and to 2.38 m/2.40 m in slant range; the PSLR was in addition measured to about 6.8 dB/6.6 dB. The advantage of a geometrical autofocus approach is clarified further by comparing the FGA algorithm to a standard strategy, in this case the Phase Gradient Algorithm (PGA).