DESPECKLING AND DETECTION OF HIGH REFLECTANCE REGIONS FROM SARIMAGES

Emmanuel Bratsolis and Marc Sigelle

Ecole Nationale Superieure des TelecommunicationsDepartement Traitement du Signal et des Images

46 rue Barrault F-75013 Paris, France(e-mails: bratsoli@tsi.enst.fr and sigelle@tsi.enst.fr)

ABSTRACT

A speckle reduction method for synthetic aperture radar (SAR)images is presented here. This method can be considered as a firststep for the extraction of other important information. Thesecondone is the detection of high reflectance regions which yieldsanimportant step to continue the segmentation of the total image.

We have worked in 3-look simulated and real ERS-1 ampli-tude images. The iterative filter is based on a membrane modelMarkov random field (MRF) approximation optimized by a syn-chronous local iterative method (SLIM). The final form of restora-tion gives a total sum preserving regularization (TSPR).

1. INTRODUCTION

Speckle noise exists in all types of coherent imaging systems andits presence reduces the resolution of the image and the detectabil-ity of the target. Speckle noise is not only signal dependentbutis also spatially correlated and reduces the effectivenessof imagereduction. A multilook SAR image is a map of amplitude modu-lations of the processed data.

Although a� distribution is adapted to SAR multilook ampli-tude images [10], a Gaussian approximation leads to a simpleit-erative algorithm preserving the mean value and decreasingaboutsix times the standard deviation of regions with different constantreflectivity.

The high reflectance regions are defined as the brightest re-gions of the image after our despeckling method.

2. DESPECKLING WITH SLIM AND TSPR

Let g andf be random fields withg the degraded observed imageandf the “true” image. The notion of a MRF extends the notionof a Markov process to multidimensional spaces by generalizingthe concept of order dependence [4], [7], [9]. A MRF is a discretestochastic process whose global properties are controlledby meansof its local conditional probabilities.

Let us note the finite lattice of sites asS = fsgs=1:::N withS � Z2. Each sites 2 S has a set of neighborsr notedNs. Ifs = (i; j) we assume in the following four-connectivity :Ns = f(i� 1; j); (i+ 1; j); (i; j � 1); (i; j + 1)g .

This research has been supported by a Marie Curie Fellowshipof theEuropean Community programme MCFI in applied mathematics undercontract number HPMF-2000-00532.

The general problem is now to estimate a random fieldf froma set of input datag. Bayes theorem allows as to obtain the poste-rior probability for the fieldf given the datagP (f jg) = P (gjf)P (f)P (g) (1)

whereP (f) is the prior probability for the fieldf , P (gjf) is theconditional probability for the datag givenf andP (g) is the prob-ability of g, which is independent off [8].

We assume now as conditional probabilityP (gjf) a Gaussiandistribution and we haveP (gjf) = exp�"Xs (fs � gs)22�2 #C1 (2)

where� is the standard deviation of the Gaussian distribution andC1 is a normalization constant. The validity of this approximationfor SAR images will be checked afterwards.

The prior probabilityP (f) is given by the membrane modelMRF [5] P (f) = exp�24�X(r;s)(fs � fr)235C2 (3)

where� is a smoothness factor,C2 a normalization constant, andthe sum runs on all pairs of neighbor sites. Thus the fieldf isconstrained to be smooth and the popular model of the first order(nearest-neighbor pairs) membrane MRF has been used. From (1)we obtain P (f jg) = 1Z exp�U(f) (4)

whereZ, also called the posterior partition function, is a normal-ization constant andU(f) is the total posterior potential function,which writes as :U(f) =Xs (fs � gs)22�2 + �X(r;s)(fs � fr)2 (5)

The related local conditional potential functions are given by:Vs(f) = (fs � gs)22�2 + � Xr2Ns(fs � fr)2 (6)

Here we accept as a fast method of optimization a synchronousminimization of the local potential energies which we namedsyn-chronous local iterative method (SLIM) and which accordingourknowledge has been used firstly in [2]. Minimizing (5) we have:@Vs(f)@fs = (fs � gs)�2 + 2� Xr2Ns(fs � fr) = 0which for a four-connectivity can be written as:fs = 11 + 8��2 gs + 2��21 + 8��2 Xr2Ns fr 8s 2 S: (7)

We write now (7) as:fs = 11 + 8��2 gs + 8��21 + 8��2 < fr > (8)

where< fr > stands for the average of the four values offr. Letus note � = 11 + 8��2 with � 2]0; 1[Equation (8) takes then the form:fs = � gs + (1� �) < fr > 8s 2 S: (9)

SLIM iterative scheme synchronously updates (9) by setting:f (n+1) = � g + (1� �) R(f (n)) 8n � 1 (10)

wheref (n) is the computed image at step(n) andR(:) is the av-erage operator regularizing the pixel intensities.A version of (9) has been used as a smoothing method preservingcartographic structuring features for SPOT images [3]. This lineariterative scheme has been shown to converge for positive values of� and� [2].

Here we are interested to regularization method for restorationpreserving the total sum of grey level values in the image.

We shall note from now on this sum asF (f) =Xs2S fs.From what precedes, this total intensity evolves as:F (f (n+1)) = � g + (1� �) F (R(f (n)))It is obvious that the operatorR(:) preserves the total sumi :e:F (R(f (n))) = F (R(f (n�1)))then iteratively:F (f (n+1)) = F (f (n)) : : : = F (f (1)) = F (g)i :e: total sum is preserved, provided that initial guessf (1) has thesame total sum than observationg. For this reason we named thismethod as total sum preserving restoration (TSPR).We assign to the preserving total intensity operatorR(:) the aver-age convolution filter associated to a normalized matrixR. Ouralgorithm takes now the formf (n+1) = � g + (1� �)R � f (n) 8n � 1 (11)

where� is the 2-D convolution operation. Thus at each step thecurrent pixel value will depend in a regularizing manner on its

neighbor ones, according to the magnitude of hyperparameter �.It is also obvious that positivity is preserved when0 � � � 1.The algorithm converges for0 < �0 � � � �1 < 1 and we ob-tain the best restoration for� = �0. For the simulated image wefind �0 = 0:08 and this is the same value that we accept for realimages coded in 16 bits.�0 has been chosen as the minimum valueof the relative error after 100 iterations of the simulated image [6].

3. OUR DETECTION METHOD

The high reflectance regions correspond to the brightest noiselesssites, so at the same time we have to detect and to test while thedetected sites are really brights or noisy.

Important role plays the threshold which is defined empiricallyasMs for the high reflectance regionsMs = MRI + 1:76 �RI (12)

whereMRI is the total mean and�RI is the total standard devia-tion of the restored image, as we can see in Fig. 4.

The high reflectance regions has been detected by (13) for 3-look simulated and real SAR amplitude imagesms �Ms (13)

wherems is the local mean of the sites calculated by a slidingwindow3� 3.

In practice we begin with an initial artificial image (Fig. 1)anda degraded image by multiplicative noise in a 3-look amplitudeversion (Fig. 2). The degraded image has been restored (Fig.3)by TSPR method (11).

We use the same filter matrixR for both real and syntheticimage: R = " 0 0:25 00:25 0 0:250 0:25 0 # :The parameter� is kept constant throughout all iterations and bechosen to0:08.The TSPR method seems to converge (to the global minimum) forevery 0:08 � � < 1 with the filterR which we have chosen.Another basic property of the TSPR method is that it preserves themean values of local homogeneous regions and decreases aboutsix times the standard deviation.

The accepted termination criterion has been given by (14)Ps jfr(n+1)s � fr(n)s j2Ps jfr(n)s j2 � 10�6 (14)

wherefr(n+1)s is the estimated image at stepn+ 1 of restorationandfr(n)s at stepn [1]. That gives the restored simulated image ofFig. 3 after 92 iterations. The segmentation result can be shown inFig. 5.An image of a specific line of our simulated scene can be shownin Fig. 6 and be compared by the noisy and the ideal signal.

A real amplitude ERS-1 image of Roissy region in France hasbeen tested. We can see that in Fig. 7. After the application ofthe TSPR method and by use of termination criterion of (14) therestoration algorithm converges after 58 iterations and the resultsare shown in Fig. 8. The detection results are given by (13) andcan be shown in Fig. 9.

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Fig. 1. Initial simulated image coded in 16 bit

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Fig. 2. Simulated image degraded by multiplicative noise

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Fig. 3. Restored simulated image

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Fig. 4. Supposed restored histogram and basic notation

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Fig. 5. Detection of the high reflectance region

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Fig. 6. Comparison of the noisy signal (dotted line), restored sig-nal (solid line) and real signal (dashed line)

Fig. 7. Initial ERS-1 c ESA image (1024 x 1024) of Roissy regionin France

Fig. 8. Restored image of Roissy region

Fig. 9. Detection of high reflectance regions of Roissy

AcknowledgmentsThe authors are grateful to H. Maitre and F. Tupin for the fruitfuldiscussions.

4. REFERENCES

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