A NEW SAR SUPERRESOLUTION IMAGING
ALGORITHM BASED ON ADAPTIVE
SIDELOBE REDUCTION
Ping Zhang, Zhen Li,Jianmin Zhou, Quan
Chen, Bangsen Tian
Center for Earth Observation and Digital Earth
Chinese Academy of Sciences
Outlines
• Problem with weighting in SAR
• 2D ASR method
• Resolution Enhancement algorithm Based
on ASR
• Results and Analysis
• Conclusion
Impact of Weighting
SAR imagery based on conventional Fourier transform (FT) techniques often requires sidelobe control
for the high sidelobes.
It has traditionally been accomplished by using window functions such as Taylor, Hanning, Hamming,
etc.
0
Rect
Hamming
Hanning
Blackman
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However, the lower sidelobes have
been achieved at the expense of
broadening the mainlobe width, i.e. it
degrades the image resolution.
dB
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ASR Method
• DeGraaf S.R. proposed ASR method to suppress sidelobes, which is a
nonlinear operator based on cosine-on-pedestal frequency domain weighting
functions, accomplished on a pixel-by-pixel basis which allows each pixel in
an image to receive its own frequency domain aperture amplitude weighting
function from a continuum of possible weighting functions.
• ASR can effectively suppress sidelobes induced by finite-aperture without
broadening the mainlobe of the impulse response. ASR takes advantage of the
fact that cosine-on-pedestal weighting functions can be implemented as a
multi-point convolution on a Nyquist sampled image.
2D ASR Method
• The weight function of 2D ASR method is as
follow
 2 mr kr
W  nr , na , kr , ka   1    w  nr , na , mr , ma  cos 
mr 1 ma 1
 kr
M
•
•
•
•
M
 2 ma ka 

cos




 ka 
Where n  0, , N 1 , n  0, , N 1, k  0, , K 1 , k  0,
w  nr , na , mr , ma  is weight coefficient,
M is the order of weight coefficients,
K r ， K a is the number of signal samples
within the signal bandwidth,
• N r ，N a is the oversample number.
r
r
a
a
r
r
a
, Ka  1
2D ASR Method
• The signal model can be expressed in frequency
filed:
Gˆ  nr , na , kr , ka   G  kr , ka W  nr , na , kr , ka 
• The signal in time filed is rewritten as
gˆ (nr , na ) 
K r 1 K a 1
  Gˆ (n , n , k , k )e
r
kr  0 ka  0
a
r
j 2
nkr
Nr
a
j 2
e
nka
Na
 g (nr , na ) 
M
M
  wn , n , m , m  S n , n , m , m 
mr 1 ma 1
r
a
r
a
r
a
r
a
2D ASR Method
• Where:
S  nr , na , mr , ma  



N
N
Nr
N
1 
mr , na  a ma   g  nr  r mr , na  a ma 
 g  nr 
4 
Kr
Ka
Kr
Ka




 

N
N
N
N
 g  nr  r mr , na  a ma   g  nr  r mr , na  a ma  
Kr
Ka
Kr
Ka

 

r 
Nr
Kr
a 
Na
Ka
• Let
,
to be oversample factor
• S  nr , na , mr , ma  can be expressed
1
 g  nr   r mr , na   a ma 
4
 g  nr   r mr , na   a ma 
S  nr , na , mr , ma  
 g  nr   r mr , na   a ma 
 g  nr   r mr , na   a ma  
2D ASR Method
• The main idea of ASR is that if the signal sample
is sidelobe, it can be identified by the data
samples around it, and suppressed using the
weights.
• The optical weights can be obtained by
minimizing the output energy of filter.
• Generally if the oversample factor  is
noninteger, the signal should be upsample to
integer sample number to make the weights
efficient.
2D ASR Method
• The choice of optical weights is derived as
followed. Rewrite the time filed signal in matric
form
gˆ  nr , na   g nr , na   wT nr , na  y nr , na 
• In order to enhance the weights degree of
freedom, we process the real component and
imaginary component of SLC image partly
• Let gˆ  nr , na   gˆr  nr , na   jgˆi  nr , na 
and y  nr , na   yr  nr , na   jyi  nr , na  .
2D ASR Method
• The output of the filter becomes
T
ˆ

g
n
,
n

g
n
,
n

w




r
r
a
1  nr , na  yr  nr , na 
 r r a

T
ˆ
g
n
,
n

g
n
,
n

w





i
r
a
2  nr , na  yi  nr , na 
 i r a
• Minimize the output energy of the filter,


 min gˆ  n , n  2
r
r
a


2
 min gˆ i  nr , na 



2D ASR Method
• Then we obtain the weights
gr  nr , na 
w  nr , na    T
yr  nr , na  yr  nr , na 
T
1
gi  nr , na 
w2  nr , na    T
yi  nr , na  yi  nr , na 
T
2D ASR Method
• In order to obtain the efficient output, consider
the l1 norm and l2 norm constraint on the
weights,
M
M
  wn , n , m , m   c
m1 1 m2 1
M
r
a
1
2
M
  wn , n , m , m 
m1 1 m2 1
r
a
1
2
1
2
1
 c2  1
• where the parameter c1 in l1 norm and
parameter c2 in l2 norm can be adjusted.
Resolution Enhancement algorithm Based on ASR
• After range direction compression, the time field signal is
Sinc function.
• If the image is integer Nyquist sampled, ASR is then
applied to the image domain samples to remove the
sidelobes directly. Otherwise the image should be
upsampled to integer Nyquist sampled image.
• Since ASR is a nonlinear operation, the resultant image
is no longer band-limited after such processing.
• When performing an inverse FFT to the ASR image, the
resultant Fourier spectral domain data will have greater
extent than the original data.
Resolution Enhancement algorithm Based on ASR
• The nonlinear ASR operation increases the original
bandwidth, but introduces a magnitude taper that
includes nulls.
• For an ideal point scatter, this taper corresponds to the
FFT of a Sinc mainlobe.
• An inverse Hamming weight is then applied to equalize
the magnitude taper over an aperture to smooth the ASR
spectrum in order to approach to the spectrum shape of
ideal point target.
• ASR operation is finally applied to the bandwidth
extrapolated Fourier spectral data to obtain a sidelobe
reduction image.
Resolution Enhancement algorithm Based on ASR
• The steps of the algorithm are shown in the following
Raw Data
General SAR
Imaging Method
SLC Image
ASR
Image after
ASR
FFT
Phase History
Data
Cosine Inverse
Weights
Extended Phase
History Data
IFFT
Image Field
ASR
Superresolution
Image
Results and Analysis
• Figures show the results of simulated point scatter using
different methods. (a) is the unwindowed Fourier image.
(b) is the imaging result using the paper’s method.
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距离向(m)
距离向(m)
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方位向(m)
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(b)
• The resolution enhancement can be shown obviously
and sidelobes are also suppressed very well.
Results and Analysis
• Table is the performance compared between the
conventional method and the paper’s method. We can
easily see the improvement in resolution, peak sidelobe
ratio (PSLR) and integral sidelobe ratio (ISLR) in two
directions.
Performance Index
Fourier Method
Paper’s Method
Range resolution(m)
1.0544
0.7983
Range PSLR(dB)
-13.4213
-26.9950
Range ISLR(dB)
-10.1341
-24.2225
Azimuth resolution(m)
1.1044
0.8270
Azimuth PSLR(dB)
-12.3295
-24.3613
Azimuth ISLR(dB)
-8.9495
-22.0205
Results and Analysis
距离向
距离向
Figures show the result of SIR-C data using different
methods. The data is obtained in 1994 of some city in
Taiwan, which data process number is 51581.
方位向
(a) RD Method
方位向 Method
(b) The Paper’s
Compared the two figures, we can see the river edge is clearer in (b). From the middle
white circle, the targets docked at the land can be distinguished easily in (b). So the
resolution can be enhanced obviously and sidelobes can also be suppressed very well.
Conclusion
• The paper provides an efficient extrapolation algorithm to
enhance resolution as well as reduce sidelobes, which is
based on ASR.
• The processing of algorithm is simple to operate.
• Simulation experiments show the validity of the
algorithm. Comparing to the Fourier method, the
proposed algorithm obtains better results.
• The image characteristics after the processing of the
paper’s method should be analyzed in the future.