Abstract:
Illumination gradients in a synthetic aperture radar (SAR) image of a target can be mitigated by determining a correction for pixel values associated with the SAR image. This correction is determined based on information indicative of a beam pattern used by a SAR antenna apparatus to illuminate the target, and also based on the pixel values associated with the SAR image. The correction is applied to the pixel values associated with the SAR image to produce corrected pixel values that define a corrected SAR image.

Description:
This invention was developed under Contract DE-AC04-94AL85000 between Sandia Corporation and the U.S. Department of Energy. The U.S. Government has certain rights in this invention. 
    
    
     FIELD OF THE INVENTION 
     The invention relates generally to Synthetic Aperture Radar (SAR) and, more particularly, to processing SAR images. 
     BACKGROUND OF THE INVENTION 
     Conventional Synthetic Aperture Radar (SAR) processing effectively forms a synthetic beam pattern that offers azimuth resolution much finer than the actual beamwidth of the antenna. Both the actual aperture (antenna) beam and the synthetic aperture beam constitute spatial filters. Proper target scene selection requires these spatial filters to be properly pointed and aligned in the desired direction. That is, the SAR scene of interest must be adequately illuminated by the actual antenna beam. 
     Furthermore, the actual antenna beam pattern rarely offers uniform illumination over its nominal width, typically taken as the angular region between its −3 dB illumination directions. Consequently, SAR images may show a reduction in brightness towards the edges of the scene being imaged. This is exacerbated whenever imaged scenes are large compared with the illumination footprint, such as at near ranges or coarse resolutions. While careful antenna calibration and alignment allows compensating for antenna beam roll-off with an inverse of the relative two-way gain function, any unexpected illumination gradients from other system sources will be left unmitigated. For example, any misalignment of the synthetic beam from the actual beam will cause unexpected brightness gradients across the image. Such misalignment might be due to factors such as the mounting of the antenna, the environment of the antenna, motion measurement errors affecting the synthetic beam orientation, near-range operation, wide scenes, or inadequate antenna pointing accuracy. Illumination anomalies are also known to be caused by atmospheric phenomena. 
     A number of conventional algorithms attempt to characterize from the data the synthetic beam direction in relation to the actual beam direction. These are generally referred to as Doppler Centroid Estimation algorithms. Generally, they are not concerned with beam shape beyond using it to calculate the Doppler frequency at the beam center. This is required to process the data correctly, especially for orbital systems. 
     Conventional techniques that correct for antenna illumination patterns in SAR images are often referred to as Radiometric Calibration techniques. When these techniques are used in orbital SAR systems, the elevation pattern is usually a significant concern, due to the favored processing methods and typically larger range swaths associated with orbital systems. In any event, the methodology is typically designed to ensure that any measured pattern matches the theoretical pattern, with the theoretical pattern being used for purposes of correcting the larger data set with a single calibration correction. 
     Some conventional techniques compensate for the antenna azimuth beam pattern during image formation processing and, in some instances, the beam pattern must be known before processing. 
     It is desirable in view of the foregoing to provide for improvements in mitigating illumination gradients in SAR images. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  graphically illustrates an illumination profile of a SAR image according to exemplary embodiments of the invention. 
         FIG. 2  graphically illustrates a vector produced by fitting the illumination profile of  FIG. 1  to a representation of a beam pattern of a SAR antenna apparatus, according to exemplary embodiments of the invention. 
         FIG. 3  graphically illustrates a normalized vector produced by normalizing the vector of  FIG. 2  according to exemplary embodiments of the invention. 
         FIG. 4  graphically illustrates an illumination correction vector produced by inverting the normalized vector of  FIG. 3  according to exemplary embodiments of the invention. 
         FIG. 5  diagrammatically illustrates a SAR system according to exemplary embodiments of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     Exemplary embodiments of the invention mitigate illumination gradients (including illumination roll-off effects) in a SAR image by fitting an antenna beam pattern model to an illumination profile of the image, and compensating the pixel brightness with an inverse relative gain function that is determined based on the model-fitting. This is accomplished without a detailed antenna pattern calibration, and provides some tolerance of drift in the antenna beam alignments. 
     In some embodiments, a SAR image is characterized by an associated two-dimensional pixel value array. The columns and rows of the two-dimensional pixel value array respectively correspond to range and azimuth directions of the SAR image. Some embodiments use a non-linear filter in the range direction of the SAR image to produce the illumination profile. For each azimuth position in the azimuth direction of the SAR image, the filter determines a representative pixel value, also referred to herein as a profile pixel value, for the column of range pixel values associated with that azimuth position. A profile pixel value is thus determined for each column in the aforementioned two-dimensional pixel value array. 
     When determining the illumination profile of the SAR image, some embodiments attempt to avoid undue influence from bright target points or shadow regions. For example, for each column, the median pixel value associated with that column can be taken as the profile pixel value for that column. The median pixel values provide an illumination profile  11 , an example of which is shown graphically in  FIG. 1 . 
     The median pixel value data of  FIG. 1  is then smoothed by fitting it to a representation of the antenna beam pattern. If the antenna beam pattern is known, then the representation that defines that pattern can be used directly. Alternatively, any suitable polynomial representation that approximates the antenna beam pattern can be used. Such an approximation can be used, for example, in situations where the antenna beam pattern is not known. An antenna beam pattern will usually exhibit a strong quadratic behavior in the neighborhood of its peak response. Subtle variations from the quadratic behavior may be captured with models that use a few higher-order terms. Various embodiments therefore use various 3 rd  or 4 th  order polynomial representations. For example,  FIG. 2  graphically illustrates the median value data of  FIG. 1  fitted to a 4 th  order polynomial representation of the antenna beam pattern. The resulting curve  21  is a data vector or array. In some embodiments, the curve fitting illustrated in  FIG. 2  is accomplished using conventional minimum-mean-squared-error techniques. 
     The vector  21  can be normalized to unit amplitude by dividing each element of the vector by the vector&#39;s maximum value. The result of this normalization is shown as a normalized vector  31  in  FIG. 3 . The inverse of the vector  31  can then be calculated by dividing each normalized vector value from  FIG. 3  into one, that is, by replacing each vector value of  FIG. 3  by its reciprocal value. This inversion operation produces pixel correction values that define an illumination correction vector, as shown at  41  in  FIG. 4 . 
     In each row of the aforementioned original two-dimensional pixel array that constitutes the original SAR image, the pixel value at each azimuth position can be corrected by multiplication with the respectively corresponding pixel correction value of the illumination correction vector  41 . The resulting corrected pixel values define a corrected SAR image. This pixel value correction operation can mitigate illumination gradients present in the original SAR image. 
     In some embodiments, the pixel value correction operation is applied to the SAR image after other brightness corrections (e.g. lookup tables, gamma corrections, etc.) have been applied. Some embodiments average illumination correction vectors  41  over several SAR images to mitigate peculiarities resulting from anomalies within a single image. 
     Note that the polynomial antenna beam pattern representation of  FIG. 2  exhibits an azimuth-oriented illumination gradient. Some embodiments utilize an antenna beam pattern representation that exhibits a range-oriented illumination gradient. 
       FIG. 5  diagrammatically illustrates a SAR system according to exemplary embodiments of the invention. In some embodiments, the system of  FIG. 5  is capable of performing operations described above with respect to  FIGS. 1-4 . The system includes a SAR data collection unit  51  coupled to a pixel corrector designated generally at  52 - 56 . The SAR data collection unit  51  uses conventional techniques to produce at  57  pixel value arrays that define respective SAR images. An illumination profile determiner  52  coupled to the SAR data collection unit  51  is configured to determine for each pixel value array at  57  a corresponding set of profile pixel values. Each set of profile pixel values defines an illumination profile  58  (e.g., the illumination profile at  11  in  FIG. 1 ) of the corresponding SAR image. A curve fitting unit  53  coupled to the illumination profile determiner  52  is configured to fit each illumination profile  58  to a suitable representation of the actual antenna beam pattern used by the SAR data collection unit  51 . The curve-fitting unit  53  produces a vector  60  of curve-fitted pixel values (e.g., the vector at  21  in  FIG. 2 ). The curve-fitting unit  53  is coupled to a normalizer  54  that is configured to normalize the curve-fitted pixel values of the vector  60 . The resulting normalized vector  61  (e.g., the vector at  31  in  FIG. 3 ) is input to an inverter  55  configured to invert the normalized pixel values of the vector  61  to produce a corresponding illumination correction vector  62  (e.g., the illumination correction vector  41  of  FIG. 4 ). A correcting unit  56  coupled to the inverter  55  and the SAR data collection unit  51  is configured to combine each illumination correction vector at  62  with its respectively corresponding SAR image at  57 , for example, in the manner described above with respect to  FIG. 4 . The resulting corrected SAR image is designated generally at  63 . 
     Although exemplary embodiments of the invention have been described above in detail, this does not limit the scope of the invention, which can be practiced in a variety of embodiments.