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

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RectHammingHanningBlackman

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.

However, the lower sidelobes have been achieved at the expense of broadening the mainlobe width, i.e. it degrades the image resolution.

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

• Where• is weight coefficient,• M is the order of weight coefficients,• ， is the number of signal samples

within the signal bandwidth,• ， is the oversample number.

1 1

22, , , 1 , , , cos cos

r a

M Ma ar r

r a r a r a r am m r a

m km kW n n k k w n n m m

k k

0, , 1 , 0, , 1, 0, , 1 , 0, , 1r r a a r r a an N n N k K k K

, , ,r a r aw n n m m

rK aK

rN aN

• The signal model can be expressed in frequency filed:

• The signal in time filed is rewritten as

2D ASR Method

ˆ , , , , , , ,r a r a r a r a r aG n n k k G k k W n n k k

11 22

0 0

1 1

ˆˆ ( , ) ( , , , )

( , )

, , , , , ,

arar

ar

r a

r a

nknkKK jjNN

r a r a r ak k

r a

M M

r a r a r a r am m

g n n G n n k k e e

g n n

w n n m m S n n m m

• Where:

• Let , to be oversample factor• can be expressed

2D ASR Method

1, , , , ,

4

, ,

a ar rr a r a r r a a r r a a

r a r a

a ar rr r a a r r a a

r a r a

N NN NS n n m m g n m n m g n m n m

K K K K

N NN Ng n m n m g n m n m

K K K K

rr

r

N

K a

aa

N

K

, , ,r a r aS n n m m

1, , , ,

4,

,

,

r a r a r r r a a a

r r r a a a

r r r a a a

r r r a a a

S n n m m g n m n m

g n m n m

g n m n m

g n m n m

• 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

• In order to enhance the weights degree of freedom, we process the real component and imaginary component of SLC image partly

• Let and .

2D ASR Method

Tˆ , , , ,r a r a r a r ag n n g n n n n n n w y

ˆ ˆ ˆ, , ,r a r r a i r ag n n g n n jg n n

, , ,r a r r a i r an n n n j n n y y y

• The output of the filter becomes

• Minimize the output energy of the filter,

2D ASR Method

T1

T2

ˆ , , , ,

ˆ , , , ,

r r a r r a r a r r a

i r a i r a r a i r a

g n n g n n n n n n

g n n g n n n n n n

w y

w y

2

2

ˆmin ,

ˆmin ,

r r a

i r a

g n n

g n n

• Then we obtain the weights

2D ASR Method

T1 T

,,

, ,r r a

r ar r a r r a

g n nn n

n n n nw

y y

T2 T

,,

, ,i r a

r ai r a i r a

g n nn n

n n n nw

y y

• In order to obtain the efficient output, consider the norm and norm constraint on the weights,

• where the parameter in norm and parameter in norm can be adjusted.

2D ASR Method

1l 2l

1 2

1 2 11 1

, , , 1M M

r am m

w n n m m c

1 2

2

1 2 21 1

, , , 1M M

r am m

w n n m m c

1c 1l2c

2l

• 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

Resolution Enhancement algorithm Based on ASR

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.

• The resolution enhancement can be shown obviously and sidelobes are also suppressed very well.

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(a) (b)

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

(a) RD Method (b) The Paper’s Method

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.

Results and Analysis

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.

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• 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.

Conclusion