Factorized Geometrical Autofocus for Synthetic Aperture Radar Processing

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)

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

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

Evaluation of a new autofocus algorithm within the framework of Fast Factorized Back-Projection

The following report deals with a new autofocus algorithm within the framework of time domain SAR processing (Fast Factorized Back-Projection). The strategy, developed at SAAB EDS, relies on varying flight track parameters until a sharp image is obtained. Focus measures are provided by a predetermined object function.After a short introduction and some preliminaries, the algorithm is described in detail, results for two different data sets (collected by the CARABAS II system) are then presented, analyzed and discussed.The analysis emphasizes some promising attributes. Two of the autofocused images are for example sharper than corresponding references. It is also shown that two of the variation parameters are separable, this reduces the required number of geometry hypotheses substantially. However, some issues are also raised. A point-like target is for example easily distorted unless the data is upsampled prior to the processing. For the moment, it is not clear if this problem is related to the back-projection or the autofocus algorithm itself. The time consumption is another distinct downside.The report concludes that a lot of work remains to be done before the algorithm can be considered as functional. A sensitivity study with respect to the variationparameters, as well as a search for alternativeobject functions should be prioritized. A more conventional autofocus approach is also proposed, to keep options open for the future

Factorized Geometrical Autofocus for Synthetic Aperture Radar Processing

Synthetic Aperture Radar (SAR) imagery is a very useful resource for the civilian remote sensingcommunity and for the military. This however presumes that images are focused. There are severalpossible sources for defocusing effects. For airborne SAR, motion measurement errors is the maincause. A defocused image may be compensated by way of autofocus, estimating and correctingerroneous 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 usuallyassumed to be space invariant and confined to one dimension. The call for relaxed requirementson inertial measurement systems contradicts these criteria, as it may introduce space variant phaseerrors 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 theFactorized 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 residualspace 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 SideLobeRatio (PSLR) values for (point/point-like) targets in FGA and reference images are similar withina few percents and tenths of a dB.As an example: the resolution of a trihedral reflector in a reference image and in an FGA imagerespectively, was measured to approximately 3.36 m/3.44 m in azimuth, and to 2.38 m/2.40 m inslant 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 FGAalgorithm to a standard strategy, in this case the Phase Gradient Algorithm (PGA)

Evaluation of a new autofocus algorithm within the framework of Fast Factorized Back-Projection

The following report deals with a new autofocus algorithm within the framework of time domain SAR processing (Fast Factorized Back-Projection). The strategy, developed at SAAB EDS, relies on varying flight track parameters until a sharp image is obtained. Focus measures are provided by a predetermined object function.After a short introduction and some preliminaries, the algorithm is described in detail, results for two different data sets (collected by the CARABAS II system) are then presented, analyzed and discussed.The analysis emphasizes some promising attributes. Two of the autofocused images are for example sharper than corresponding references. It is also shown that two of the variation parameters are separable, this reduces the required number of geometry hypotheses substantially. However, some issues are also raised. A point-like target is for example easily distorted unless the data is upsampled prior to the processing. For the moment, it is not clear if this problem is related to the back-projection or the autofocus algorithm itself. The time consumption is another distinct downside.The report concludes that a lot of work remains to be done before the algorithm can be considered as functional. A sensitivity study with respect to the variationparameters, as well as a search for alternativeobject functions should be prioritized. A more conventional autofocus approach is also proposed, to keep options open for the future

Factorized Geometrical Autofocus at UHF-band

This paper describes an autofocus experiment at UHF-band. That is within the scope of factorized geometrical autofocus (FGA). The FGA algorithm is a base-2 fast factorized back-projection (FFBP) formulation with six free geometry parameters (per sub-aperture pair). These are tuned step-by step until a sharp image is obtained. This innovative autofocus technique can compensate completely for an erroneous geometry. The FGA algorithm has been applied successfully on an UWB data set, acquired by the LORA system (i.e. at UHF band). Before processing, we add errors due to a constant quadratic bias to the measured track. This emulates a drifting inertial measurement unit (IMU) and motivates the use of autofocus. The resulting FGA image is compared to a reference image and verified to be focused (even sharper actually). Hence, the FGA algorithm is fit for use at UHF-band