Autofocus and analysis of geometrical errors within the framework of fast factorized back-projection

This paper describes a Fast Factorized Back-Projection (FFBP) formulation that includes a fully integrated autofocus algorithm, i.e. the Factorized Geometrical Autofocus (FGA) algorithm. The base-two factorization is executed in a horizontal plane, using a Merging (M) and a Range History Preserving (RHP) transform. Six parameters are adopted for each sub-aperture pair, i.e. to establish the geometry stage-by-stage via triangles in 3-dimensional space. If the parameters are derived from navigation data, the algorithm is used as a conventional processing chain. If the parameters on the other hand are varied from a certain factorization step and forward, the algorithm is used as a joint image formation and autofocus strategy. By regulating the geometry at multiple resolution levels, challenging defocusing effects, e.g. residual space-variant Range Cell Migration (RCM), can be corrected. The new formulation also serves another important purpose, i.e. as a parameter characterization scheme. By using the FGA algorithm and its inverse, relations between two arbitrary geometries can be studied, in consequence, this makes it feasible to analyze how errors in navigation data, and topography, affect image focus. The versatility of the factorization procedure is demonstrated successfully on simulated Synthetic Aperture Radar (SAR) data. This is achieved by introducing different GPS/IMU errors and Focus Target Plane (FTP) deviations prior to processing. The characterization scheme is then employed to evaluate the sensitivity, to determine at what step the autofocus function should be activated, and to decide the number of necessary parameters at each step. Resulting FGA images are also compared to a reference image (processed without errors and autofocus) and to a defocused image (processed without autofocus), i.e. to validate the novel approach further

An Efficient Solution to the Factorized Geometrical Autofocus Problem

This paper describes a new search strategy within the scope of factorized geometrical autofocus (FGA) and synthetic-aperture-radar processing. The FGA algorithm is a fast factorized back-projection formulation with six adjustable geometry parameters. By tuning the flight track step by step and maximizing focus quality by means of an object function, a sharp image is formed. We propose an efficient two-stage approach for the geometrical variation. The first stage is a low-order (few parameters) parallel search procedure involving small image areas. The second stage then combines the local hypotheses into one global autofocus solution, without the use of images. This method has been applied successfully on ultrawideband CARABAS II data. Errors due to a constant acceleration are superposed on the measured track prior to processing, giving a 6-D autofocus problem. Image results, including resolution, peak-to-sidelobe ratio and magnitude values for point-like targets, finally confirm the validity of the strategy. The results also verify the prediction that there are several satisfying autofocus solutions for the same radar data

Factorized Geometrical Autofocus for Synthetic Aperture Radar Processing

This paper describes a factorized geometrical autofocus (FGA) algorithm, specifically suitable for ultrawideband synthetic aperture radar. The strategy is integrated in a fast factorized back-projection chain and relies on varying track parameters step by step to obtain a sharp image; focus measures are provided by an object function (intensity correlation). The FGA algorithm has been successfully applied on synthetic and real (Coherent All RAdio BAnd System II) data sets, i.e., with false track parameters introduced prior to processing, to set up constrained problems involving one geometrical quantity. Resolution (3 dB in azimuth and slant range) and peak-to-sidelobe ratio measurements in FGA images are comparable with reference results (within a few percent and tenths of a decibel), demonstrating the capacity to compensate for residual space variant range cell migration. The FGA algorithm is finally also benchmarked (visually) against the phase gradient algorithm to emphasize the advantage of a geometrical autofocus approach