Resolution-Preserving Two-Look Despeckling of SAR Images

Junfeng Wang and Xingzhao LiuShanghai Jiaotong University, China

junfengwang@sjtu.edu.cn and xzhliu@sjtu.edu.cn

Abstract: An improved two-look processing is presented todespeckle Synthetic Aperture Radar (SAR) images. Theazimuth spectrum is halved after a constant phase is removed. Each half is extrapolated conjugate symmetrically to form afull-band azimuth spectrum, and the full-band azimuthspectrum is used to generate a look. Then, the two looks areaveraged incoherently to obtain a two-look image. In thisalgorithm, not only the speckle is suppressed but also theresolution is preserved.

Key words: SAR, Speckle, Multilook Processing.

I. INTRODUCTION

Owing to coherence, Synthetic Aperture Radar (SAR)images are affected by speckle. This is undesired in manyapplications. Various algorithms are presented to despeckle SAR images. Typical algorithms can be classified into twocategories, the multilook processing [1-2] and the locally-statistical processing [3-6]. The latter are classified into twosubcategories, the minimum-mean-square-error processing[3-5] and the maximum-likelihood processing [5-6]. Thesealgorithms are summarized in [7-8].

In the original two-look processing, the azimuthspectrum is halved, each half is used to generate a look, and then the two looks are averaged incoherently to obtain atwo-look image. In the incoherent averaging, the speckle issuppressed because the speckles in the two looks areindependent. However, since each look has a half-bandresolution only, the two-look image has a half-bandresolution only.

We present an improved two-look processing todespeckle SAR images. The azimuth spectrum is halvedafter a constant phase is removed. Each half is extrapolated conjugate symmetrically to form a full-band azimuthspectrum, and the full-band azimuth spectrum is used togenerate a look. Then, the two looks are averagedincoherently to obtain a two-look image. In the incoherentaveraging, the speckle is suppressed because the specklesin the two looks are independent. In addition, the resolution of the image is preserved. Since each look has a full-bandresolution, the two-look image has a full-band resolution.

II. RESOLUTION-PRESERVING TWO-LOOKDESPECKLING

A. FoundationLet a(x,R) be the complex speckled image, where x and

R are azimuth coordinate and slant range, respectively.Then,

a(x,R)=[s(x,R)+n(x,R)]exp[jϕ(R)]. (1)

s(x,R) and n(x,R) are the speckleless image and the speckle, respectively. An additional phase ϕ(R) is contained in (1)because such an R-dependent phase may not be removedin SAR imaging. Multiplying (1) by exp[−jϕ(R)] yields

a(x,R)exp[−jϕ(R)]=s(x,R)+n(x,R). (2)

Taking the Fourier transform of (2) with respect to x, weobtain

A(u,R)exp[−jϕ(R)]=S(u,R)+N(u,R), (3)

where A(u,R), S(u,R) and N(u,R) are the Fourier transforms of a(x,R), s(x,R) and n(x,R) with respect to x, respectively, and u is the x-wavenumber.

Assume that f(x,R) and h(x,R) are the scatteringcoefficient of the target field and the point spread function of the system, respectively. Then, s(x,R) can be expressedas the convolution of f(x,R) and h(x,R), i.e.,

s(x,R)=f(x,R)∗h(x,R). (4)

f(x,R) is real. In addition, we assume that the SARprocessor is designed such that h(x,R) is real. (Otherwise,additional procedures can be carried out to obtain a realh(x,R).) Since both f(x,R) and h(x,R) are real, s(x,R) is real. Thus, we conclude that S(u,R) is conjugate symmetricabout u=0, i.e.,

S(u,R)=S*(−u,R). (5)

As we will see, a resolution-preserving two-lookdespeckling algorithm can be developed according to thisproperty.

B. AlgorithmIn the resolution-preserving two-look despeckling

algorithm, the next steps are carried out for each range bin.

(1) Find A(u,R)exp[−jϕ(R)]. ϕ(R) is estimated using thealgorithm in part C of section II.

(2) Generate a look from A(u,R)exp[−jϕ(R)], u≤0. First, a full-band azimuth spectrum is formed by extrapolatingA(u,R)exp[−jϕ(R)], u≤0. That is,

⎩⎨⎧

>ϕ−−≤ϕ−

=0,)]}(exp[),({0)],(exp[),(

),( *1 uRjRuAuRjRuA

RuA . (6)

0-7803-9582-4/06/$20.00 ©2006 IEEE

When u≤0, A1(u,R)=A(u,R)exp[−jϕ(R)]. When u>0, A1(u,R)is got by reversing and conjugating A(u,R)exp[−jϕ(R)],u<0. Then, a look is generated by applying the inverseFourier transform to A1(u,R) with respect to u.

As shown in (3), A(u,R)exp[−jϕ(R)] consists of S(u,R)and N(u,R). They correspond to the speckleless image and the speckle, respectively. Since S(u,R) is conjugatesymmetric about u=0, a full-band S(u,R) is formed in theconjugate-reversal extrapolation. Therefore, this look has a full-band resolution. On the other hand, the speckle in thislook is entirely determined by A(u,R)exp[−jϕ(R)], u≤0.

(3) Generate a look from A(u,R)exp[−jϕ(R)], u≥0. First, a full-band azimuth spectrum is obtained by extrapolatingA(u,R)exp[−jϕ(R)], u≥0. That is,

⎩⎨⎧

<ϕ−−≥ϕ−

=0,)]}(exp[),({0)],(exp[),(

),( *2 uRjRuAuRjRuA

RuA . (7)

When u≥0, A2(u,R)=A(u,R)exp[−jϕ(R)]. When u<0, A2(u,R)is got by reversing and conjugating A(u,R)exp[−jϕ(R)],u>0. Then, a look is generated by applying the inverseFourier transform to A2(u,R) with respect to u.

As shown in (3), A(u,R)exp[−jϕ(R)] consists of S(u,R)and N(u,R). They correspond to the speckleless image and the speckle, respectively. Since S(u,R) is conjugatesymmetric about u=0, a full-band S(u,R) is formed in theconjugate-reversal extrapolation. Therefore, this look has a full-band resolution. On the other hand, the speckle in this look is entirely determined by A(u,R)exp[−jϕ(R)], u≥0.

(4) Average the two looks incoherently to obtain a two-look image. In the incoherent averaging, the speckle isreduced because the speckles in the two looks areindependent. In addition, since each look has a full-bandresolution, the two-look image has a full-band resolution.

C. Estimation of ϕ(R)ϕ(R) needs to be evaluated in step (1) of part B of

section II. It can be calculated according to the parameters of the system. It can also be estimated using the algorithmin figure 1. In this algorithm, ϕ′(R), the estimate of ϕ(R), is adjusted to minimize a cost function by trial and error.

ϕ′(R) is initialized as ∠A(0,R), the phase of A(0,R).Letting u=0 in (3), we obtain

A(0,R)exp[−jϕ(R)]=S(0,R)+N(0,R). (8)

S(0,R) is much stronger than N(0,R), and thus

A(0,R)exp[−jϕ(R)]≈ S(0,R). (9)

Since S(0,R) is real, we obtain

ϕ(R)≈∠A(0,R). (10)

Thus, we can use ∠A(0,R) as the initial value of ϕ′(R).

The cost function is defined as

duRjRuA

RjRuA2*

0

)]}(exp[),({

)](exp[),(

ϕ′−−

−ϕ′−=ε ∫∞

. (11)

Actually, ε is a measure of the conjugate symmetry ofA(u,R)exp[−jϕ′(R)] about u=0. It is the minimum 0 whenA(u,R)exp[−jϕ′(R)] is conjugate symmetric about u=0. Itincreases when A(u,R)exp[−jϕ′(R)] deviates from theconjugate symmetry about u=0. When ϕ′(R) equals ϕ(R),it is assumed that A(u,R)exp[−jϕ′(R)] is closest to theconjugate symmetry about u=0, and therefore ε is aminimum. When ϕ′(R) deviates from ϕ(R), it is assumedthat A(u,R)exp[−jϕ′(R)] deviates from the conjugatesymmetry about u=0, and therefore ε increases.

Figure 1. Estimation of ϕ(R).

III. RESULTS

A complex image is used to evaluate our algorithm. The data were obtained from the Danish EMISAR system. Wethank the Technical University of Denmark for providingthe data. Actually, similar results are also obtained fromother data.

Figure 2 shows the one-look image. Evidently, theimage is speckled. Figure 3 shows the original two-lookimage. We can see that the speckle is suppressed but theresolution is lost. Figure 4 shows the improved two-lookimage. As we can see, not only the speckle is suppressedbut also the resolution is preserved.

ϕ′(R)⇐∠A(0,R). ε is computed.

ϕ′(R)⇐ϕ′(R)−0.01. ε is computed.

ε decreases?Y

ϕ′(R)⇐ϕ′(R)+0.01.N

ϕ′(R)=∠A(0,R)?

ϕ′(R)⇐ϕ′(R)+0.01. ε is computed.

ε decreases?Y

ϕ′(R)⇐ϕ′(R)−0.01.N

Yε is updated.

N

Start

End

Figure 2. One-Look Image.

Figure 3. Original Two-Look Image.

Figure 4. Improved Two-Look Image.

The contrast of an image g(x,R) is defined as

)],([)],([

RxgRxgC

μσ= . (12)

μ[g(x,R)] and σ[g(x,R)] are the mean and the standarddeviation of g(x,R), respectively. Contrast can be used tomeasure the resolution and the speckle of an image [1-2,9]. It is larger when the resolution is higher and thespeckle is stronger. The improved two-look image and the one-look image have the same resolution. However, theformer has weaker speckle than the latter. Therefore, weconclude that the contrast of the improved two-look image is less than that of the one-look image. The improved two-look image has as weak speckle as the original two-lookimage. However, the former has a higher resolution thanthe latter. Therefore, we conclude that the improved two-look image has a larger contrast than the original two-lookimage. By calculation, the contrasts of the one-look image, the original two-look image and the improved two-lookimage are 0.718552, 0.576148 and 0.709865, respectively. This confirms our conclusions.

IV. CONCLUSIONS

The improved two-look processing has betterperformance than the original two-look processing indespeckling SAR images. In the original two-lookprocessing, the speckle is reduced, but the resolution is lost. However, in the improved two-look processing, not onlythe speckle is reduced, but the resolution is preserved aswell.

REFERENCES

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