Abstract:
A method of synthetic aperture radar autofocus for ground penetration radar. The method includes transmitting a signal via an antenna; receiving a reflected signal comprising a plurality of image blocks via the antenna; reading each image block from the reflected signal via a processor; locating prominent targets in each image block via the processor; estimating ground penetration phase error via the processor in each image block via phase error inputs including pulling range and quantization level by generating a 1D phase error and converting the 1D phase error into a 2D phase error of an image spectra; refocusing each image block according to estimated ground penetration phase error for that image block via the processor; and forming an image mosaic comprising each refocused image block via the processor.

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention is related to U.S. Government contract number H94003-04D-0006 Task Order 0185 (Hawkeye (Ground Penetrating Synthetic Aperture Radar (GPSAR)) Vertical Take Off and Landing). The U.S. Government has certain rights in this invention. 
    
    
     BACKGROUND 
     1. Field 
     The present invention is related to autofocus for ground penetration radar (“GPR”), and more particularly to, autofocus for wide-beam/wide-band GPR. 
     2. Description of Related Art 
     Synthetic aperture radar (“SAR”) is used for ground mapping as well as target identification, where a moving platform, e.g., an aircraft, has an imaging radar that sends transmitted signals from different positions along the path of the platform such that the ground (e.g., ground clutter) reflects signals that are received by the imaging radar. 
     To achieve high azimuth resolution in SAR image formation, the slant range history of the processed target must be highly accurate. However, high azimuth resolution is not achieved for most SAR systems, since a costly high performance navigation system would be required, as well as accurate knowledge of the terrain elevation. One viable solution is to include an autofocus process during or after SAR processing for improving the image quality. 
     However, though there are some autofocus solutions for various narrow band and narrow beam SAR systems, the autofocus solution for GPR remains a challenging problem due to several factors. First, the autofocus solution is highly spatially varying within the image frame. For a narrow beam SAR, one autofocus solution is mostly applicable to the entire image. But, for a wide beam SAR, one autofocus solution may only be applicable to a small image block. This is because the phase error caused by the navigation error is angle dependent, as illustrated in  FIGS. 2 and 3 . 
     As show in  FIG. 2 , the distance from the target  200  to the actual aircraft path  202  may deviate from the knowledge aircraft path  204  by a range error  206 . 
     As shown in  FIG. 3 , 
     dRA=R′A−RA, 
     dRB=R′B−RB, 
     dRA≠dRB, 
     where dRA is the difference between the distance from the radar actual position  30  to target A and the distance from the radar knowledge position to target A, and where dRB is the difference between the distance from the radar actual position  30  to target B and the distance from the radar knowledge position to target B. Here, dRA and dRB are not equal. 
     Second, the target range migration trace of a wide beam SAR is highly curved due to the wide synthetic aperture angle. In range compressed data, it is difficult to extract a target signal directly or after a simple data deskew process. Therefore, identifying prominent targets or estimating phase error cannot be efficiently performed in the range compressed data set. 
     Third, the strength of the prominent targets in GPR is usually not as high as other high frequency SAR. This leads to the need for highly sensitive phase error estimation algorithms, such as maximum likelihood estimation or contrast optimization. 
     All these factors indicate the need for an effective GPR autofocus method. 
     SUMMARY 
     Embodiments of the present invention are related to an autofocus method for wide-beam/wide-band GPR. This method estimates target phase error directly from a complex ground image of high contrast targets. A focused image is then obtained by removing the estimated phase error from the spatial frequency spectra of the complex image. The phase error of the imaged targets is modeled by the superposition of a one-dimensional (1D) Fourier series of limited order. Each component of the phase error is estimated from the two-dimensional spatial (ground) frequency spectra through 2D to 1D mapping. Optimal phase error is obtained by means of a contrast optimization method. 
     An embodiment of the present invention provides a method of synthetic aperture radar autofocus for ground penetration radar. The method includes transmitting a signal via an antenna; receiving a reflected signal comprising a plurality of image blocks via the antenna; reading each image block from the reflected signal via a processor; locating prominent targets in each image block via the processor; estimating ground penetration phase error via the processor in each image block via phase error inputs including pulling range and quantization level by generating a 1D phase error and converting the 1D phase error into a 2D phase error of an image spectra; refocusing each image block according to estimated ground penetration phase error for that image block via the processor; and forming an image mosaic comprising each refocused image block via the processor. 
     The estimating ground penetration phase error may further include: assigning an order of base functions via the processor; assigning a phase error magnitude via the processor; generating the 1D phase error from the assigned phase error magnitude and the base function via the processor; generating a 2D image spectra via a 2D fast fourier transform of each image block via the processor; mixing the 2D phase error over the 2D image spectra via the processor; performing an inverse 2D fast fourier transform over the phase error mixed spectra to determine an image domain via the processor; determining phase error among multiple phase error magnitudes and multiple image blocks based on maximum image contrast; determining a total phase error based on phase error components via the processor; and removing the total phase error from the image spectra via the processor. 
     Another embodiment of the present invention provides a system for synthetic aperture radar autofocus for ground penetration radar. The system includes: an antenna for transmitting a signal and for receiving a reflected signal comprising a plurality of image blocks, and a processor. The processor is programmed to: read each image block from the reflected signal; locate prominent targets in each image block; estimate ground penetration phase error in each image block via phase error inputs including pulling range and quantization level by generating a 1D phase error and converting the 1D phase error into a 2D phase error of an image spectra; refocus each image block according to estimated ground penetration phase error for that image block; and form an image mosaic comprising each refocused image block. 
     The processor may further be programmed to estimate ground penetration phase error further by: assigning an order of base functions; assigning a phase error magnitude; generating the 1D phase error from the assigned phase error magnitude and the base function; generating a 2D image spectra via a 2D fast fourier transform of each image block; mixing the 2D phase error over the 2D image spectra; performing an inverse 2D fast fourier transform over the phase error mixed spectra to determine an image domain; determining phase error among multiple phase error magnitudes and multiple image blocks based on maximum image contrast; determining a total phase error based on phase error components; and removing the total phase error from the image spectra. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The patent or application file contains at least one color drawing executed in color. Copies of this patent or patent application with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. 
         FIG. 1A  is a schematic view of an aircraft with an SAR according to an embodiment of the present invention. 
         FIG. 1B  is a schematic view of the SAR of  FIG. 1A . 
         FIG. 2  is a schematic view of a source of range error. 
         FIG. 3  is a schematic view of an angle dependent range error. 
         FIG. 4  is a schematic view of spectra of a complex GPR image. 
         FIG. 5  is a schematic view of mapping geometry of a GPR. 
         FIG. 6  is a flow chart showing a method of autofocus data flow according to an embodiment of the present invention. 
         FIG. 7  is a flow chart showing a method of GPR phase error estimation data flow according to an embodiment of the present invention. 
         FIG. 8  shows an original unfocused impulse response for a simulated point target with a first injected phase error. 
         FIG. 9  shows a simulated phase error for the target of  FIG. 8 . 
         FIG. 10  shows a spectra mask for the target of  FIG. 8 . 
         FIG. 11  shows a focused impulse response for the target of  FIG. 8  after a method of autofocus according to an embodiment of the present invention. 
         FIG. 12  shows a phase error base function for the target of  FIG. 8  resultant from a method of autofocus according to an embodiment of the present invention. 
         FIG. 13  shows an estimated phase error for the target of  FIG. 8  resultant from a method of autofocus according to an embodiment of the present invention. 
         FIG. 14  shows an original unfocused impulse response for a simulated unfocused point target with a second injected phase error. 
         FIG. 15  shows a simulated phase error for the target of  FIG. 14 . 
         FIG. 16  shows a spectra mask for the target of  FIG. 14 . 
         FIG. 17  shows a focused impulse response for the target of  FIG. 14  after a method of autofocus according to an embodiment of the present invention. 
         FIG. 18  shows a phase error base function for the target of  FIG. 14  resultant from a method of autofocus according to an embodiment of the present invention. 
         FIG. 19  shows an estimated phase error for the target of  FIG. 14  resultant from a method of autofocus according to an embodiment of the present invention. 
         FIG. 20   a  shows an unfocused GPR image with corner reflectors, where the system has a wide frequency band from 1.0 GHz to 1.8 GHz. 
         FIG. 20   b  shows an enlarged area I of  FIG. 20   a.    
         FIG. 20   c  shows an example of a focused impulse response of the image of  FIG. 20   a  according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     An embodiment of the present invention provides a method for autofocus for wide-beam/wide-band ground penetration radar (GPR), where the wide beam angle makes the phase error highly spatially varying. This method estimates target phase error directly from the complex ground image of high contrast targets. A focused image is then obtained by removing the estimated phase error from the spatial frequency spectra of the complex image. The phase error of the imaged targets is modeled by the superposition of a one-dimensional Fourier series of limited order. Each component of the phase error is estimated from the two-dimensional spatial (ground) frequency spectra through 2D to 1D mapping. Optimal phase error is obtained by means of a contrast optimization method. 
     Embodiments of this method overcome some of the challenges of GPR autofocus. First, to overcome spatially varying phase error, the GPR image is divided into multiple image blocks in order for each image block to be refocused by a single phase profile. A phase error estimate is independently applied to each image block. An optional trending analysis may be applied to all estimated phase error functions for further improvement before phase error is finally applied to refocus the image. 
     Embodiments of this method are suitable for ground penetration radar for detecting natural resources and for medical tomography image processing. 
     According to an embodiment of the present invention, a moving platform  120  (e.g., an airplane) has an imaging radar, shown in  FIG. 1A , that sends a transmitted signal  124  such that the ground  126  (e.g., ground clutter) reflects a reflected signal  122  that is received by the imaging radar  101 . As show in  FIG. 1B , the imaging radar  100  includes an antenna  102  that receives a signal from a transmitter  104  for transmission as a transmitted signal  124  and that receives the reflect signal  122  for a receiver  106 . A processor  108  performs an autofocus method according to an embodiment of the present invention. 
     A text or graphical terminal input device  110  allows the user to enter or key in the processing parameters for both image formation and autofocus. An output device  112  outputs or prints the processing log and intermediate parameters as feedback to the user. An image display device  114 , such as a monitor, allows the user to examine the SAR image and the phase error plots. All processed images, estimated phase error data, processing log files may also stored in a storage device  116 . 
     The highly curved target range migration trace prevents the efficient use of the range compressed data for autofocus. Therefore, embodiments of the present invention perform a phase error estimate from the 2D spectra of the complex ground image, which show that there is a simple relationship between the one-dimensional slant range error and the two-dimensional phase error spreading over a fan shaped area in the spatial frequency domain. In this mapping, the synthetic aperture time is related to the polar angle of the spectra. The slant range error is related to a 2D phase error according to the wave number or the spatial frequency in the radial direction of the spectra. 
     To overcome the lower signal-to-noise ratio of a GPR target, a preferred solution for phase error estimation is taken, i.e. image contrast optimization. In addition, a target screening process is employed to allow the most useful point-like target be selected for phase error estimation. 
     One can express the phase error Δφ(t) in terms of base function expansion, 
               Δφ   ⁡     (   t   )       =       ∑     i   =   1     I     ⁢       a   i     ⁢       L   i     ⁡     (   t   )                 
where L i (t) is the base function and a i  is the associated coefficient. Here, there may be many choices of base functions. One example is the Legendre orthogonal polynomial, as described in U.S. Pat. No. 7,145,496 to Cho et al. This base function is favored due to the fact that a common phase error term is a quadratic one. However, since the linear term does not introduce any focusing artifact, it must be excluded from the base function. In addition, the Legendre orthogonal polynomial is more complicated when it involves the high order terms. Our proposed base function for the phase error model is the Fourier series with cos(2π i t) and sin(2π i t) terms in the following form:
 
     
       
         
           
             
               Δφ 
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 I 
               
               ⁢ 
               
                 ( 
                 
                   
                     
                       a 
                       i 
                     
                     ⁢ 
                     
                       cos 
                       ⁡ 
                       
                         ( 
                         
                           2 
                           ⁢ 
                           πⅈ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           t 
                         
                         ) 
                       
                     
                   
                   + 
                   
                     
                       b 
                       i 
                     
                     ⁢ 
                     
                       sin 
                       ⁡ 
                       
                         ( 
                         
                           2 
                           ⁢ 
                           πⅈ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           t 
                         
                         ) 
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
     The advantage of this base function is that there is a simple mapping between each sidelobe location and each pair of cos(2π i t) and sin(2π i t) base function. The value of a i  and b i  are bounded by two input parameter. These are the pulling range, φ max , or the error bound, and the quantization level Δφ. The number of phases compared in this system is an integer ceil(φ max /Δφ), and the computation load is proportional to ceil(φ max /Δφ). One way to reduce computation load is by using a multiple stage of phase comparison scheme, which involves a coarse phase quantization in the initial stage and a fine quantization in the subsequent stages. 
     The focus degradation of a target in GPR originates from the error in the estimate of the target delay time Δτ(t), where 
               Δτ   ⁡     (   t   )       =       2   c     ⁢   Δ   ⁢           ⁢     R   ⁡     (   t   )               
and ΔR(t) is the range error between the actual slant range and the knowledge slant range derived from the navigation data. The associated phase error of Δτ(t) with respect to the center frequency of the radar pulse is given by
 
     
       
         
           
             
               
                 Δφ 
                 c 
               
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 - 
                 
                   
                     4 
                     ⁢ 
                     π 
                   
                   
                     λ 
                     c 
                   
                 
               
               ⁢ 
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               
                 R 
                 ⁡ 
                 
                   ( 
                   t 
                   ) 
                 
               
             
           
         
       
     
     The phase error viewed in the ground spatial frequency domain is give by 
               Δφ   ⁡     (       k   rg     ,       θ   polar     ⁡     (   t   )         )       =         -   2     ⁢   π   ⁢           ⁢     k   rg     ⁢   Δ   ⁢           ⁢     R   ⁡     (   t   )         =       -   4     ⁢   π   ⁢       cos   ⁢           ⁢       θ   gz     ⁡     (   t   )         λ     ⁢   Δ   ⁢           ⁢     R   ⁡     (   t   )                 
where k rg =cos θ gz (t)·k r  and
 
               k   r     =       2   λ     .           
The polar angle in spatial frequency coordinate is related to the ground azimuth angle of the target, i.e. θ polar (t)=π−θ az (t). Both the ground azimuth angle and the grazing angle are given by θ az (t)=tan −1 (({right arrow over (r)} T (t)−{right arrow over (r)} ac (t))·Ĉ, ({right arrow over (r)} T (t)−{right arrow over (r)} ac (t))·{right arrow over (v)} ac (t 0 )) where Ĉ is the cross-track unit vector. Further,
 
                 θ   gz     ⁡     (   t   )       =       sin     -   1       ⁡     (         -     (           r   -&gt;     T     ⁡     (   t   )       -         r   -&gt;       a   ⁢           ⁢   c       ⁡     (   t   )         )       ·     d   ^                    r   -&gt;     T     ⁡     (   t   )       -         r   -&gt;       a   ⁢           ⁢   c       ⁡     (   t   )                )             
where {circumflex over (d)} is the unit vector of the down-track.
 
     The along-track unit vector is given by â={right arrow over (v)} ac (t 0 )/∥{right arrow over (v)} ac (t 0 )∥ and {circumflex over (d)}=â×Ĉ. 
     The polar angle of the target, at time t, is given by θ polar (t)=π−θ az (t). The complex image spectra and the mapping geometry are illustrated in  FIGS. 4 and 5 . 
     The image quality can be described by the impulse response in terms of 3 dB resolution and sidelobe level. In an SAR system where residual phase error exists, the peak of the impulse response drops, the 3 dB width increases, and the sidelobe level is raised. All these impulse response performance factors lead to the reduction of image sharpness and contrast. A conventional contrast measure is in the form of 
               ∑   i     ⁢       A   i   4     /       (       ∑   i     ⁢     A   i   2       )     2             
which is referred to as the 5th metric by Muller and Buffington in the September 1974 article in the JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, Vol. 64, No. 9, entitled, “Real-time correction of atmospherically degraded telescope images through image sharpening,” the entire content of which is incorporated herein by reference. This is a highly nonlinear measure. It assigns a much larger weight to a brighter target. This has the effect of making medium and low intensity targets, nearby the brighter target, unable to influence the final phase error estimate. Further, a contrast metric may be formulated such that targets falling into a certain intensity range dominate the final contrast measures, as described by J. R. Fienup and J. J. Miller in the April 2003 article in the JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, Vol. 20, No. 4, entitled, “Aberration correction by maximizing generalized sharpness metrics,” the entire content of which is incorporated herein by reference. Therefore, one may perform autofocus based on various targets such as prominent point targets, a complicated urban target, or a vegetation area.
 
     The problem with the conventional contrast metric design is that there is only one contrast metric for each scene. This can be avoided by using the concept of local contrast, which is the contrast measure of small image patches or segments of image lines. The idea of local contrast has been carefully studied and found to be practical. 
     The high level autofocus method is illustrated in  FIG. 6 . Since the phase error of a GPR system is spatially varying, refocusing a large GPR image may be performed in a loop with each small image block focused independently. The method begins by reading an individual image block k  602 . To estimate the phase error of each image block with maximum efficiency, the prominent target must be identified  604 . The prominent target should have sharp features in the azimuth dimension with good signal to background noise ratio. Next, the GPR phase error estimation is performed  606 . Here, phase error inputs are pulling range and quantization level  608 . Then, refocusing of image block k is performed. Next, it is determined whether there are more image blocks to be read  612 . After all image blocks are refocused, a final image is formed as the mosaic of the refocused image blocks  614 . 
     The core autofocus process using the contrast optimization consists of two “do” loops. The first one is the loop over all orders of Fourier series of interest. The second is the loop over all levels of phase error magnitude within the pulling range. Details of the process of steps  606  and  607  are illustrated in the data flow diagram in  FIG. 7 . 
     This process consists of the following steps: assigning the order of the base function  702 ; assigning the phase error magnitude  704 ; generating the 1D phase error from the assigned phase error magnitude and the base function  706 ; converting the 1D phase error into a 2D phase error of the image spectra  708 ; generating a 2D image spectra by a 2D FFT  714  over the selected image block  712 ; mixing the 2D phase error over the 2D image spectra  710 ; and performing inverse 2D FFT  716  over the phase error mixed spectra to get back to the image domain  718 . At the end of phase error magnitude loop  720 , the matched magnitude with the maximum contrast is identified  722 . At the end of the base function loop  724 , all phase error components for the final phase error are added  726 . Once the final phase error is estimated, the final phase error is then removed from the image spectra in a step similar to step  710  above. 
     The algorithm described above was implemented on PC workstation in both Matlab and c language. Tests have been performed using simulated complex images with injected phase error as well as tests using real GPR image data, which indicate that this method is a viable solution to the GPR autofocus problems described above. 
       FIG. 8  shows an original unfocused impulse response for a simulated unfocused point target with an injected phase error,  FIG. 9  shows a simulated phase error for the target of  FIG. 8 , and  FIG. 10  shows a spectra mask for the target of  FIG. 8 .  FIG. 8  shows the simulated point target ground image with an injected phase error spreading over an area shown as the spectra mask. The target is out of focus with multiple bright dots. 
       FIG. 11  shows a focused impulse response for the target of  FIG. 8  after a method of autofocus according to an embodiment of the present invention,  FIG. 12  shows a phase error base function for the target of  FIG. 8  resultant from the method, and  FIG. 13  shows an estimated phase error for the target of  FIG. 8  resultant from the method. The unfocused target is refocused into a single dot with very little sidelobes. The estimated phase error is substantially identical to the injected phase error. 
     A second example with a different injected phase error is shown in  FIGS. 14 to 19 .  FIG. 14  shows an original unfocused impulse response for a simulated unfocused point target with a second injected phase error,  FIG. 15  shows a simulated phase error for the target of  FIG. 14 , and  FIG. 16  shows a spectra mask for the target of  FIG. 14 .  FIG. 17  shows a focused impulse response for the target of  FIG. 14  after a method of autofocus according to an embodiment of the present invention,  FIG. 18  shows a phase error base function for the target of  FIG. 14  resultant from the method, and  FIG. 19  shows an estimated phase error for the target of  FIG. 14  resultant from the method. Here, the unfocused target is refocused into a single dot with small sidelobes. The estimated phase error is substantially identical to the injected phase error. 
     Real GPR images have also been successfully tested with the proposed autofocus algorithm.  FIG. 20   a  shows an unfocused GPR image with corner reflectors, where the system has a wide frequency band from 1.0 GHz to 1.8 GHz,  FIG. 20   b  shows an enlarged area I of  FIG. 20   a , and  FIG. 20   c  shows an example of a focused impulse response of the image of  FIG. 20   a  according to an embodiment of the present invention. The impulse response of the corner reflector in the original image is smeared with relatively poor resolution in azimuth. A small image block with nine corner reflectors is tested with the autofocus method. Here, the refocused corner reflectors all become much sharper impulse responses with 3 dB resolution consistent with the predicted value and improved sidelobe ratio. 
     Other tests were also successful for other GPR images with different bandwidth ranges and other types of scenes with or without man-made targets. 
     Embodiments of the present invention provide an accurate and effective autofocus method for the ground penetration radar. By applying autofocus independently over each image block, the spatially varying phase in a wide beam GPR is overcome. An accurate phase error model is formed by the mapping between the target slant range errors over time to the 2D phase error over polar angle in the spectra domain. Accurate phase error is estimated by using the image contrast optimization over each phase error component within a Fourier series of limited order. 
     Although the present invention has been described and illustrated in respect to exemplary embodiments, it is to be understood that it is not to be so limited, and changes and modifications may be made therein which are within the full intended scope of this invention as hereinafter claimed.