Automated Robust Procedure for SAR Image Filtering and Preliminary Analysis

Vladimir V. Lukina, Nikolay N. Ponomarenkoa, Sergey K. Abramova, Karen O. Egiazarianb, Jaakko T. Astolab

aNational Aerospace University, Kharkov, Ukraine bSignal Processing Institute, Tampere University of Technology, Finland

ABSTRACT In some practical situations it is often necessary to process radar images for which a priori information about noise characteristics is limited. Evaluating these characteristics, in particular, estimating speckle noise variance, is quite a complicated and time consuming task. In order to carry out both tasks efficiently enough for typical practical situations an automated robust procedure for SAR image filtering and preliminary analysis is proposed. It consists of several stages: a) blind evaluation of speckle relative variance for the original image, b) pre-processing using the local statistic Lee filter, c) blind evaluation of the residual noise relative variance for the pre-processed image, d) post-filtering. It is shown that the proposed procedure provides rather accurate estimations of noise characteristics. The effectiveness of the filtering scheme is confirmed for both simulated and real scene SAR images. Keywords: SAR image filtering, automated robust procedure

1. INTRODUCTION It is an important task to develop such methods of preliminary analysis of noise characteristics in radar images and such techniques of image filtering that possess sufficient accuracy and efficiency and simultaneously minimize user�s subjec-tive influence on the undertaken decisions1. In other words, the methods of image analysis and processing should be robust in wide sense.2 Let us give a few examples of such situations. First, it might happen that one deals with radar images of unknown origin or does not have information about the characteristics of a radar that was used in forming those images. For instance, the images can be formed by some synthetic aperture radar (SAR) with unknown number of looks.1 Second, one has to test the newly designed software intended for radar image processing using a set of different real radar images.3 Then the question is how to accurately estimate the basic characteristics of multiplicative noise in these images. Third, the quality of original image is poor (and this is typical for SAR images, especially if the number of looks is small) and it is strongly desirable to suppress speckle in order to enhance the image. This task can, for exam-ple, arise if the image is further subject to visual analysis, registration with other images of the same terrain, warping to topography map, etc.1 It is clear that any kind of a priori knowledge about noise characteristics is able to improve the performance of many image processing methods. For the considered case of radar image processing, a priori information about multiplicative noise probability density function (pdf) and relative variance is valuable for edge detection4, spike detection and re-moval5,6 (if impulsive noise is present in the original images). The a priori knowledge of multiplicative noise variance is also very important for image filtering. It is worth mentioning here that according to conclusions based on performance comparison carried out for different filters applicable to radar image processing7,8, the best results have been obtained for the filters that in one or another manner take into account the relative variance of multiplicative noise. The examples of such filters are the widely known and commonly used local statistic Lee and Frost filters9,10. Another examples are the recently designed methods based on wavelet and discrete cosine transforms.8,11,12 All aforementioned methods of radar image filtering have one common drawback. They are unable to remove impulsive noise that can corrupt the SAR image simultaneously with speckle.13 Recently we have proposed several filtering tech-niques (locally adaptive and iterative ones) able to cope with mixed multiplicative+impulsive noise.13-18 However, all these methods require the a priori known or pre-estimated value of multiplicative noise variance. In particular, this is needed for setting the proper threshold for locally adaptive filters.13,17 Moreover, some of these methods are applicable

SAR Image Analysis, Modeling, and Techniques V, Francesco Posa, Editor,Proceedings of SPIE Vol. 4883 (2003) © 2003 SPIE · 0277-786X/03/$15.00

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for processing radar images corrupted by only Gaussian multiplicative noise13,14,18 (this is not the case for SAR images when the number of looks is small). On the contrary, the locally adaptive filters specially designed for processing SAR images with known particular (for example, Rayleigh) pdf of speckle have the parameters of their blocks13,17 optimized for given pdf. Because of this, they can not be successfully applied for filtering SAR images with other statistical char-acteristics of speckle. In this sense the most robust are the iterative filtering procedures proposed in our papers.15,16 Based of these methods described below we design automated robust procedures for SAR image filtering. The basic assumptions concerning the properties of radar images to be analyzed and processed are the following:

1) speckle (multiplicative noise) is the dominating factor degrading the radar image quality, i.e. the influence of additive noise and quantization errors can be neglected;

2) the image can be also corrupted by impulsive noise; concerning its properties it is supposed that the probability of spike occurrence is approximately equal for each pixel and this probability is not larger than 0.01;

3) the speckle can be spatially correlated but the correlation is essential for only 2x2 neighboring pixels in image homogeneous regions.

As seen, all these assumptions are quite typical for real life radar (SAR) images1,3. As for other properties of noise in radar image to be processed, they can be arbitrary. That is, we assume that speckle pdf can obey Gaussian, Gamma, Rayleigh, one-side exponential or some other �intermediate� distributions. In other words, it is supposed that the num-ber of looks used while forming the SAR image is unknown. The spatial autocorrelation function of speckle is also sup-posed to be a priori unknown, although we assume that it has rather narrow main lobe (obeying the condition given in item 3) and rather low level of side lobes. For practical radar remote sensing systems these, not so strict assumptions, are generally valid. Thus, our goal is to design an automated robust procedure for SAR image processing and preliminary analysis. It should be robust in two senses. First, it should provide appropriately effective filtering of SAR images irrespectively to real pdf of speckle. Second, this procedure has to be able to remove the impulsive noise if it is present in given SAR image and its properties obey the condition imposed by item 2. The designed procedure should be automated in the sense that it does not presume the presence of human being for performing such operations as, for instance, evaluation of multiplica-tive noise variance, estimation of speckle spatial autocorrelation function and its parameters, proper selection of filter type and its parameters like scanning window size, etc.

2. REQUIREMENTS TO SAR IMAGE FILTERING The requirements in SAR image filtering as well as in processing of other kinds of images are contradictory13. It is nec-essary to simultaneously suppress noise in image homogeneous regions (to effectively reduce speckle for the considered SAR image case), to remove spikes, to preserve edges and fine details. Often it is also desirable to provide good compu-tational efficiency. Texture preservation is also important.19 The peculiar requirement in the case of just SAR image processing is also to retain the image mean level in image ho-mogeneous regions. It follows from the fact that the image mean in homogeneous regions is strictly connected with the sensed object radar cross section (taking into account system calibration). In turn, the radar cross section depends upon different characteristics of the sensed terrain, and the retrieval of these characteristics is the prime task of remote sens-ing.1 The latter requirement in combination with unknown and, probably, non-Gaussian pdf of speckle as well as possible presence of impulsive noise imposes severe restrictions on application of many widely known filters to the task of automated SAR image processing. Of course, there exist many filters that are able to remove spikes and that do not re-quire any information about noise pdf and its parameters. Examples of such filters are the standard median, the Wil-coxon and α-trimmed filters, different versions of FIR-median hybrid filters and the weighted median filter5. However, their application to processing of SAR image with unknown properties even in the best case does not lead to the appro-priate performance trade-off. In the worst case, the use of those non-adaptive robust filters results in considerable loss of useful information contained in radar images. Really, the application of the standard median filter to image processing leads to removal of small-sized objects (de-tails) that are �considered� as impulsive noise.5 Besides, standard median filter considerably distorts texture19 and �cuts� the sharp corners of large size objects5,20. The Wilcoxon filter21 as well as the α-trimmed filters5 considerably

Proc. of SPIE Vol. 4883 49

distort (smear) the edges and fine details. Their application can result in considerably biased mean level in image ho-mogeneous regions if the speckle pdf differs from Gaussian.22 Note that we consider the case of SAR image processing for which it is quite probable that multiplicative noise has non-Gaussian distribution.23 Other robust nonlinear filters that are non-adaptive and perform image smoothing in one iteration have other drawbacks (see reference24 for details). This means that among non-adaptive one-iteration robust filters it is practically impossible to find a filter whose per-formance satisfies all the aforementioned requirements. Therefore, it seems reasonable to design the automated robust procedure for SAR image processing on basis of locally adaptive and/or iterative (multistage) filtering techniques.15,16

3. BLIND ESTIMATION OF SPECKLE VARIANCE

As it was mentioned earlier, the local statistic Lee filter9 and the Frost filter10 possess many advantages that can be very useful for SAR image processing. First, they can be applied to filtering radar images corrupted by speckle with different pdf.15,24 Irrespectively of statistical characteristics of multiplicative noise, the mean level in image homogeneous regions is retained well enough, and this is a very attractive property of these filters. Second, the local statistic Lee and Frost filters are very good in the sense of edge/detail preservation.10,24 Due to this, they also do not distort texture features too much.19 The speckle in image homogeneous regions is suppressed quite well by these two filters even if the multiplica-tive noise is spatially correlated.16,17,24 One more advantage of these filters is that after their application the residual noise becomes quasi-Gaussian in image homogeneous regions16 even if in the original image it had a non-Gaussian pdf. Nevertheless, the residual noise remains multiplicative. As an example, the histogram of the noisy values in homogeneous image region for the case of speckle Rayleigh pdf is shown in Fig. 1,a (i.i.d. speckle noise was simulated, spikes were not present). The histogram for the same homogene-ous region after image processing by the local statistic Lee filter is represented in Fig. 1,b. Obviously, the pdf of resid-ual noise has become rather close to Gaussian.

a) b)

Fig.1 Histograms of image values for homogeneous regions: a) in original image; b) after its processing by the local statistic Lee filter with the scanning window size 7x7 pixels

However, the local statistic Lee and Frost filters have several drawbacks. First, they are not robust with respect to im-pulsive noise and such robustness is necessary for the considered image/noise model. Another disadvantage is that their speckle suppression efficiency is not ideal, and suppression of residual noise is needed, e.g., by iterative processing of SAR images 11,12, 15,16,24. In this matter, the following two questions arise: 1) What should be the filter scanning window size (how to set or to select it within the framework of automated SAR image processing procedure)? 2) How to evaluate automatically the speckle noise variance in an original image? The answer to the first question is given in Section 4. Let us now answer the second question. Fortunately, till now several automatic (blind) methods for speckle variance evaluation have been already designed (see the papers 25,26,3 and references therein). Commonly, such methods are multistage and they presume the execution of the following basic steps:

1) divide the image under consideration into rather small overlapping or non-overlapping blocks; 2) get a set of local estimates of relative variance of multiplicative noise for all blocks; 3) process this set of estimates in order to get the final estimation of speckle noise variance.

50 Proc. of SPIE Vol. 4883

The assumption behind these procedures is that quite many block variance estimates correspond to blocks belonging to image homogeneous regions. It is worth saying here that for the m-th block the multiplicative noise variance estimate

2� mµσ is derived as 22 /� mm Iσ where 2�mσ is the local variance estimated for the m-th block and mI denotes the m-th block mean. Such block variance estimates corresponding to image homogeneous region blocks are supposed to slightly differ from each other, thus forming the maximum (peak) of block variance estimate histogram.25,26 To prove that it is really so let us consider the test image presented in Fig. 2. The noise-free (true) image is shown in Fig. 2,a. In its upper part there is a large homogeneous region (black color, pointed by digit 1) for which all the true values tr

ijI are equal. Such homogeneous region can correspond to water basin like a lake or a wide river in practice of radar remote sensing. Below there are some other regions that visually also seem homogeneous (denoted by digits 2 and 3). But, in fact, the true values tr

ijI for them are slightly different and these regions simulate quasi-homogeneous objects like meadows, agricultural fields, etc. More light color objects in the central part of the test image are also homogene-ous, i.e. having equal tr

ijI . Besides, the test image contains prolonged (small sized) objects that in practice can corre-spond to roads, gas and oil pipes, etc. Finally, there is also a texture region (pointed by digit 4) in the left lower corner of the test image that can correspond to different types of terrain with vegetation like forests, gardens, etc. So, using this test image one can get idea about performance characteristics of different image processing/analysis methods.

a)

b)

Fig.2. The artificial test noise-free image (a) and the same image corrupted by the Rayleigh pdf speckle (b)

The artificial test image corrupted by multiplicative noise is represented in Fig. 2,b. The pixel values have been simu-lated as ij

trijij II µ= where ijI is the ij-th pixel of the noisy image, ijµ denotes the multiplicative noise with the mean

equal to unity and relative variance 2µσ . For the image in Fig. 2,b the speckle pdf was

0),2/exp()/()( 222 ≥−= µσµσµµρ where σ is the parameter equal to 0,798 and 273,02 =µσ . This is the Rayleigh pdf of noise and it corresponds to the radar images formed by one-look SAR where the spatial distribution of backscattered signal amplitudes is imaged. For the image in Fig. 2,b the i.i.d. speckle was simulated.

Proc. of SPIE Vol. 4883 51

The histogram of the obtained block variance estimates 2� mµσ , blNm ,...,1= for the noisy image in Fig. 2,b is demon-strated in Fig. 3. The size of non-overlapping blocks was 7x7 pixels, the leftmost interval minimum is equal to 0, the rightmost interval maximum is 1.1. The histogram part for estimates larger than 1.1 is not presented. It is clearly seen that the majority of 2� mµσ concentrate in the neighborhood of the true value 0.273. The estimates form-ing the distribution tail mainly correspond to the blocks positioned on object edges and small sized objects. If the im-pulsive noise is present in the considered image, then for the blocks, for which the spikes occur, the block variance es-timates also relate to distribution tail with high probability.

Fig. 3. The histogram of block variance estimates 2� mµσ for entire image in Fig. 2,b.

Taking into account these properties of the distribution of block variance estimates it seems reasonable to estimate the histogram maximum and to choose the corresponding coordinate as the estimate 2�µσ . This idea was utilized in the method proposed in our paper26. More in detail, the proposed method consists of several steps. The first step is to get a preliminary estimate 2� prelµσ as the Q-th order statistic of the sample of block variance estimates 2� mµσ , blNm ,...,1= ,

where ξ=blNQ / , ξ is a parameter. The next step is to find the myriad value27 of the sample 2� mµσ , blNm ,...,1= .

Recall that sample myriad is the M�estimate obtained when using )log()( 22 yky +=ς as the cost function. The

parameter k is calculated as 2� prelk µσς= , ς is a parameter. The myriad is then accepted as the final estimates 2� finµσ . For this method, several parameters have to be selected or adjusted: the block size, the parameters ξ and ς . Also over-lapping or non-overlapping blocks may be used. Our investigations (some results are given in paper 26) have shown the following:

1) in the considered situation of possible spatial correlation of speckle it is worth using the 7x7 block size; 2) it is better to use overlapping blocks since this produces better accuracy of estimates 2� finµσ ;

3) the parameter ξ should be within the limits from 0.15 to 0.25, the choice 2.0=ξ can be recommended for the proposed automated procedure;

4) the appropriate values of the parameter ς are 0.04�0.1, the choice 06.0=ς is recommended for applica-tion in practice.

To characterize the accuracy of the proposed procedure of estimating speckle variance, statistical simulations have been performed. In the absence of impulsive noise, the expectation of 2� finµσ (obtained for different large fragments of the

test image) differs from the true value 2µσ by -15�+5%; the RMSE of estimates 2� finµσ is about 0.3,�,0.6%. If the

probability of impulsive noise impP =0.01 (uniform pdf of spikes within the limits 0,�,255 for 8 bit image representa-

52 Proc. of SPIE Vol. 4883

tion has been analyzed) the difference between expectation of 2� finµσ and 2µσ is from -12% to +15%, the RMSE of es-

timates is a little larger - about 0.7%. Both the expectation and the RMSE of estimates 2� finµσ become larger if there are spikes in images. It is worth noting that in other papers dealing with automatic estimation of noise variance in images the case of possible impulsive noise has not been studied. In general, the accuracy of the method depends upon many factors: the characteristics of speckle, the impulse noise probability, the size and the characteristics of the true image, etc. The accuracy becomes worse if: a) the speckle is more intensive, i.e. the value 2

µσ is large; b) impulse noise is present and its probability impP is large; c) the image size, i.e. the total number of an image (analyzed fragment) pixels is small, d) the image (or its analyzed fragment) contains many details and texture regions. The analysis of the accuracy is far from complete, however, the results presented above and given in 26 are promising. The question then is the following � is the provided accuracy of automatic estimation of speckle variance sufficient for good performance of image filtering based on the use of the obtained estimations.

4. PROPOSED AUTOMATED PROCEDURE

An automatic procedure of preliminary image analysis having the goal to get the estimates 2� finµσ of speckle variance is the first stage of the proposed automated procedure of SAR image processing. The next step is image filtering. Among two filters � local statistic Lee and Frost ones � we propose to use the former one. The motivations in favor of this rec-ommendation are the following: a) for larger 2

µσ (and this is the most difficult practical situation to deal with) the local statistic Lee filter suppresses multiplicative noise more effectively15; b) the local statistic Lee filter is better in the sense of texture preservation19; c) the local statistic Lee filter �preserves� the spikes and does not smear them in contrast to the Frost filter16,24, and this property is important from the point of view of the next stages of the proposed automated pro-cedure of image processing.

Recall that the output of the local statistic Lee filter9 is defined as

])1/[())(( 22222ijijijijijij

Leeij IIIII σσσσ µµ +−−+= , (1)

where 2ijσ is the local variance calculated for the ij-th position of the МxМ scanning window center. As seen, if 2

ijσ is

approximately equal to 22µσijI (that happens for image homogeneous regions if the impulse is absent for given scanning

window position) the locally statistic Lee filter performs as the standard mean filter. If for given ij-th position the condi-tion 2

ijσ >> 22µσijI holds, then the output value Lee

ijI differs from ijI only slightly. This means that the local statistic

Lee filter does not essentially change the original image values if 2ijσ >> 22

µσijI , i.e. in the neighborhoods of edges,

small sized objects, spikes and in textural regions. On the other hand, because of this property the local statistic Lee filter is unable to remove impulsive noise. Now, the parameter 2

µσ is used in the expression (1) denoting the output of the local statistic Lee filter. Since in prac-

tice we do not know the true value of this parameter, the only way out is to use the value 2� finµσ estimated at the previ-

ous stage in expression (1) instead of 2µσ . Thus, it is important to analyze in what degree the errors of 2

µσ estimate influence the performance of the local statistic Lee filter. To get an idea about this, we have used the standard quantitative criterion of filtering efficiency, namely, peak signal to noise ratio (PSNR). For the test image presented in Fig. 2,a the input and output image PSNRs have been calculated as

Proc. of SPIE Vol. 4883 53

∑∑= =

−=I

i

J

j

trijijinp IJIIPSNR

1 1

22 )]/)(/[255lg(10 , (2)

)]/)(/[255lg(101 1

22∑∑

= =

−=I

i

J

j

trij

Leeijout IJIIPSNR , (3)

where I and J denote the entire image size, and it is supposed that the images are represented using 8 bit integers. The initial PSNRinp were equal to 19.19 dB with assumed no impulsive noise and 18.58 dB for the case of uniformly distributed impulsive noise with 01.0=impP . The obtained values PSNRout for the case of 7x7 local statistic Lee fil-

ter are presented in Table 1. Several values of 2� finµσ have been used in (1) instead of 2µσ , the ratios 22 /� µµ σσ fin are also

given in Table 1. Table 1. PSNRout at the output of the local statistic Lee filter

22 /� µµ σσ fin 0=impP 01.0=impP

0.9 27.07 25.89 1.0 27.22 26.13 1.1 27.26 26.30

As seen, the application of the local statistic Lee filter in both cases ( 0=impP and 01.0=impP ) greatly improves the

PSNRout. The influence of impulsive noise presence is well seen since the values PSNRout for the case 01.0=impP

are approximately 1 dB smaller than for the case 0=impP . At the same time the influence of estimation errors of

speckle variance 2� finµσ is not considerable. The difference of the obtained values PSNRout for the considered range of

ratios 22 /� µµ σσ fin is about 0.2�0.4 dB. This means that the errors in 2µσ estimation of about 10% (and this is the typi-

cal level of errors provided by the automatic procedure described in Section 3) do not considerably influence the filter performance. Moreover, if the estimates 2� finµσ are larger than 2

µσ better PSNRout has been obtained. This is because the considered test image contains quite many image homogeneous regions. If the percentage of locally active areas, i.e. textural regions, edge and detail neighborhoods, in the image is larger than in the test image in Fig. 2,a the results can be opposite. Above we have given the numerical simulation results for the 7x7 scanning window. This size is recommended by us for practical application within the framework of the automated procedure of SAR image processing. The reasons for this are the following. For many filters like standard median or some other order statistic filters the increasing of the scanning window size commonly results in worse edge/detail preservation.5,24 At the same time the increasing of the scanning window size from 5x5 to 7x7 practically does not make worse the edge/detail preservation ability of the local statistic Lee filter � see the numerical simulation results in our paper.15 But the scanning window size increasing leads to better speckle suppression in image homogeneous regions15. And this is especially desirable because in the case of spatially correlated noise the noise suppression ability of practically all nonlinear filters is worse than for the case of i.i.d. speckle17,22. Since in practice one can deal with either spatially correlated or i.i.d. speckle then taking into account the aforementioned dependences it seems reasonable to set the scanning window size fixed and equal to 7x7 pixels. If the local statistic Lee filter is applied at the second stage of the proposed automated procedure of SAR image process-ing then the last task we have to solve is how to remove the remaining impulsive noise. One less important task is to additionally reduce the residual noise. The ways how to do this are already proposed and considered in our papers15,16. The first method is to apply the FIR hybrid median filter28 (modification 3LH+) to the output of the local statistic Lee filter. This filter has the fixed scan-

54 Proc. of SPIE Vol. 4883

ning window size (5x5) and it does not require any a priori knowledge about noise characteristics, in particular, the rela-tive variance of residual multiplicative noise 2

resσ in the considered case. The second technique is to apply the modified sigma filter14 to the output of the local statistic Lee filter.16 In this case one needs to a priori know or to pre-estimate the parameter 2

resσ . For this purpose the same automatic procedure as the one described in Section 3 can be applied. The

experiments have shown that the obtained estimates 2� resσ are biased and usually they are smaller than the true value 2restrueσ . However, typically they are within the limits [0.75 2

restrueσ ; 1.0 2restrueσ ].

First of all, let us present the numerical simulation results proving that the application of such iterative filtering is expe-dient. Suppose 22� µµ σσ =fin and this value is used at previous stage; the obtained values of PSNRout for images ob-

tained after local statistic Lee filter application are given in Table 1 for the row 1/� 22 =µµ σσ fin . The values of

PSNRout for two-stage filtering are presented in Table 2. Since instead of the true value of residual noise relative vari-ance its estimate 2� resσ is used to calculate the modified sigma filter output, we give two values of PSNRout that corre-spond to marginal values of estimates.

Table 2. PSNRout for two-stage (iterative) procedures

Type of filter used at stage 2 0=impP 01.0=impP

FIR hybrid median 27.39 27.14 Modified sigma, 1/� 22 =restrueres σσ 27.54 27.34

Modified sigma, 75.0/� 22 =restrueres σσ 27.56 27.34

Comparing the results presented in Tables 1 and 2 the following conclusions can be obtained:

1) the FIR hybrid median filter only slightly improves PSNRout in case of impulsive noise absence; but in the case 01.0=impP the obtained benefit is about 1 dB;

2) the modified sigma filter improves PSNRout better than FIR hybrid median filter for both cases 01.0=impP

and 0=impP , in aggregate the PSNR improvement in comparison to original (noisy) images is 8�9 dB;

3) certainly, the presence of impulsive noise appears itself in difference of the values PSNRout for the cases of spike presence and absence, although it is not large; this means that for the considered characteristics of mixed noise in SAR images the proposed procedure possesses appropriate robustness with respect to spikes.

It might seem that 2

resσ can be determined using the estimates of 2� finµσ obtained earlier. Indeed, in paper15 we present

some numerical simulation results. Moreover, in Table 3 below we also give the values of parameter 22 / µσσδ res= calculated for the local statistic Lee filter with the scanning window sizes 5x5 and 7x7. The speckle is supposed to be i.i.d. The values 2

µσ equal to 0.0225, 0.04, 0.0625 and 0.09 correspond to Gaussian multiplicative noise whilst 2µσ =0.273 relates to Rayleigh pdf of speckle.

Table 3. The values δ characterizing the noise suppression efficiency of the local statistic Lee filter

in image homogeneous regions Scanning window

size 2µσ =0.0225 2

µσ =0.04 2µσ =0.0625 2

µσ =0.09 2µσ =0.273

5х5 0.0638 0.0631 0.0628 0.0621 0.0569 7х7 0.0342 0.0340 0.0339 0.0335 0.0308

Proc. of SPIE Vol. 4883 55

However, speckle in real SAR images can be non-Gaussian and its 2µσ can be equal to, for example, 0.16 as it is for the

real SAR considered below. Besides, for spatially correlated speckle the noise suppression efficiency of the local statis-tic Lee filter depends upon parameters of spatial autocorrelation function of noise, in particular, its main lobe width. Since we do not know a priori and do not presume to estimate the parameters of spatial autocorrelation function it be-comes impossible to calculate the residual noise relative variance as 22 �� µσδσ =res . Thus, the only way out to apply the modified sigma filter to the output of the local statistic Lee filter within the frame-work of automated procedure becomes to evaluate 2� resσ using the method described in Section 3. Since, as it was men-

tioned earlier, the mean of estimates 2� resσ is smaller than the true value we propose to use the value 22 �2.1 ressigma σσ = as the input parameter of the modified sigma filter. This recommendation also follows from numerical simulation re-sults and recommendations presented in our paper.16 One more question is which filter � FIR hybrid median or modified sigma � to apply for image post-processing at the final stage. Concerning this, our recommendation is the following: if the estimated 2� resσ is larger than 0.01 then it is reasonable to apply the 7x7 modified sigma filter, otherwise the FIR hybrid median filter should be used at the final stage. This can be explained by the following. If the speckle in original image is intensive then the residual noise is also rather intensive after local statistic Lee application. Thus, the primary task is to further suppress noise and 7x7 modified sigma filter performs this considerably better than FIR hybrid median filter. In opposite situation, i.e. if the residual noise is not intensive, the primary task is to preserve edges, details and texture. Thus, the application of FIR hybrid me-dian filter is preferable. Besides PSNR, one more quantitative criterion widely used to characterize the image filtering procedure performance is the degree of noise suppression in image homogeneous regions. This can be, for example, the earlier introduced pa-rameter 22 / µσσδ res= . The smaller δ , the better the speckle reduction efficiency. As seen from Table 3, the applica-tion of the 7x7 local statistic Lee filter to SAR image corrupted by i.i.d. speckle for the case of impulsive noise absence provides speckle reduction by 5.5�32 times. Note that the most efficient speckle reduction is observed if multiplicative noise in original image is intensive, i.e. 2

µσ is large. The FIR median hybrid filter ensures additional suppression of residual noise by 1.5�2 times.15 The modified sigma filter provides reduction of residual noise by 2�3 times. In case the speckle in original image is not i.i.d. the noise reduction efficiency of the two-stage filtering procedures is poorer. However, even for spatially correlated noise the speckle variance reduction by 10�60 times can be provided15 and the best efficiency is observed just for the case of intensive speckle in original image. Therefore, summarizing the results and recommendations presented above, the proposed automated procedure of SAR image processing and analysis can be described as the following sequence of operations:

1) evaluate the relative variance of multiplicative noise in original image; for this purpose divide this image into overlapping 7x7 blocks, calculate for all blocks the set of block variance estimates 2� mµσ , blNm ,...,1= , sort

this sample and obtain the preliminary estimate 2� prelµσ as the Q-th order statistic where blNQ 2.0= , calcu-

late the parameter 2�06.0 prelk µσ= and using this value derive the myriad of the set of block variance esti-

mates 2� mµσ , accept the obtained value as 2� finµσ (see the details in Section 3);

2) apply the 7x7 local statistic Lee filter (1) to the original image substituting 2� finµσ instead of 2µσ ;

3) evaluate 2� resσ for the obtained pre-filtered image according to the method given in item 1;

56 Proc. of SPIE Vol. 4883

4) compare 2� resσ to the threshold value 0.01; if 01.0� 2 <resσ apply the FIR hybrid median filter to the output of

the local statistic Lee filter; otherwise calculate 22 �2.1 ressigma σσ = and apply the 7x7 modified sigma filter us-

ing 2sigmaσ as the input parameter instead of 2

µσ . As seen, none the operations requires participation of an expert or a User in the process of image processing and analy-sis and, thus, the proposed procedure can be executed automatically. Let us now illustrate the results of its application to artificial test image in Fig.2,b. The image in Fig. 4,a is obtained after 7x7 local statistic Lee filter application. As seen, the details and texture are preserved well whilst the speckle in image homogeneous regions is also suppressed. Additional suppression of residual noise is provided due to application of the 7x7 modified sigma filter (see Fig. 4,b), at the same time the details, edges and texture are preserved well enough.

a)

b) Fig.4 The output images for 7x7 local statistic Lee filter (a) and the proposed automated procedure (b)

Let us also demonstrate one example for real SAR data. The original SAR image �Dnieper� is shown in Fig. 5,a. The obtained estimates are 12.0� 2 =prelµσ and 15.0� 2 =finµσ . The value 2�µσ has been also estimated by us for several

selected image homogeneous regions and it is approximately equal to 0.16, so the automatic estimate 2� finµσ and �expert�

estimate 2�µσ are quite close. After processing of this real image by the 7x7 local statistic Lee filter the automatic esti-

mate 2� resσ is equal to 0.011 whilst the �expert� estimate is 0.013. Following the proposed approach we used

0132.02 =sigmaσ as the input parameter for the 7x7 modified sigma filter. The obtained image is represented in Fig. 5,b. As seen, the speckle noise is effectively suppressed (its relative variance in image homogeneous regions has been reduced by approximately 55 times). The edges and fine details are preserved well enough.

5. CONCLUSIONS

The automated robust procedure for SAR image processing (analysis and filtering) is proposed. It can be used for proc-essing SAR images with unknown pdf of speckle, both i.i.d. or spatially correlated multiplicative noise as well as for

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mixed speckle+impulsive noise environment. The proposed procedure provides efficient processing of SAR images in the sense of speckle reduction, spike removal, preservation of edges, details and texture. It can be implemented in a pipeline manner. Besides, the designed methods of speckle variance evaluation can be used for other applications, for example, to perform primary image recognition, edge and detail detection, etc., i.e. in cases the knowledge of statistical characteristics of multiplicative noise is required.

a)

b)

Fig.5 The original real SAR image (a) and the output image obtained using the proposed automated procedure (b)

6. ACKNOWLEDGEMENT

This research has been partly supported by the Project 1659 of Scientific Technology Center of Ukraine.

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