PolSAR Image Speckle Reduction Based on Polarimetric Decomposition and Classification Ping Han*, Fei Dong, Renbiao Wu *Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300 P.R. China e-mail:
[email protected] Abstract On account of the inherent speckle in PolSAR (Po larimetric Synthetic Aperture Radar) images and target scattering properties maintaining after speckle suppressing, an effective algorith m for speckle reduction based on scattering model is developed. First, fast alternative to H/α is used in PolSA R image decomposition, and total back-scattering power is co mbined for initial p ixel classification. Then, minimu m distance measure and h ierarch ical cluster method are used for further classification. Finally, p ixels are filtered according to their classes. Experimental results with AIRSAR data show that, the new algorithm is more effective than Scattering-ModelBased speckle filter developed by Lee not only in speckle reduction but also in polarimetric properties preservation. Keywords: PolSA R image, speckle reduction, fast alternative to H/α, polarimetric decomposition, classification 1. Introducti on By transmitting and receiving different polarized signals , PolSA R (Po larimetric Synthetic Aperture Radar) presents a better capability of gaining surface features which enlarge its application areas such as search and rescue of wrecked planes [1][2] . But the inherent speckle of SA R images cause image edge fuzzy easily and impact the stability of target features. Usually, search and rescue based on SAR is performed with the local scattering properties of wrecked p lane. So it’s important to protect the polarimetric properties and structure characters when doing the filtering. The representative algorithms of PolSA R image speckle [3] reduction include: Polarimetric Whitening Filter and Opti[4] mally Weighted Filter , etc. In these algorith ms, only the diagonal elements of the covariance matrix are treated, polarimetric properties of target in SA R image can’t be retained. Also, the use of fixed filtering window usually induces edge fuzzy. Scattering-Model-Based speckle filter based on mini[5] mu m mean square erro r rule was developed by Lee . By this method, pixels are classified after Freeman decomposition. It assures the filtered pixels to be of the same or similar scattering mechanism. Polarimet ric properties and texture features can be preserved effectively. Because of the comp lex terrain scattering objects generally have random orientation, so scattering echoes often have a certain stochastic fluctuation; this will induce an error during initial classification when the original data is decomposed directly by this algorith m. In addition, Freeman decomposition is supposed to be reflection symmetry which is not rotation invariant. Th is will bring an interpret error for the art ificia l objects and the filtering results will be effected.
To overcome the above problems in literature [5], an effective algorith m of speckle reduction for PolSAR images is [6] proposed in this paper. First, fast alternative to H/α is used in image decomposition, total back-scattering power is used together to perform the in itial classification. Then, minimu m [7] distance measure and hierarchical cluster method are applied to further classification. Pixels which are not point or curve-linear targets are filtered to keep target texture features. Polarimetric properties are kept better because that the pixels taking part in filtering are weighted according to the distances between their classes and the centre pixel class. ü h/q 2. Fast Alternatives to H/αü 2.1. H/α In Po lSA R image analysis, target image is often presented by polarimetric covariance mat rix C o r coherency matrix T. By Cloude-Pottier deco mposition to the coherency matrix, parameters are obtained to describe polarimetric characteristics, such as entropy H, scattering angle and anisotropy A, [8] etc. They can be shown as follows : 3 (1) H p log p
i 1
i
3
3
i
pi cos 1 ( U i )
(2)
i 1
A
pi i
3
i 1
i
p2 p3 p2 p3
(3)
. i (i=1,2,3)denotes the ith eigenvalue of the
coherency matrix, U i is the ith eigenvector. H denotes the randomness of scattering media fro m isotropic scattering (H=0) to comp letely rando m scattering (H= 1). stands for the mean scattering mechanism fro m surface scattering to double-bounce scattering. A reflects the relationship of the two weaker scattering components.This item can distinguish smaller disparity more accurately. H/α eigenspace can be divided into 8 effective reg ions bonding the values of H and α shown in Fig. 1. 2.2 h/q There are two problems in Cloude-Pottier decomposition: (1) is possibly instable. If coherency mat rix T is formed as T=zI (z is a constant, I is identity matrix), the eigenvector is o o not unique, making fluctuate in extent [54.7360 , 60 ]. If the value of H is high, this s mall range may also cause wrong classification. (2)The method for solving eigenvalues by eigen-decomposition is complicated.
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To solve the above problems, e igenvalues can be calculated from the following method [6]. (4) I T 0
3 a 2 b c 0
(5)
a (T11 T22 T33 ) where * * * .
b T11T22 T11T33 T22T33 T12T12 T13T13 T23T23 c T denotes the determinant of matrix. According to Cardano’s
formula, the eigenvalues of coherency matrix are: 1 real (( y1 y2 )1 3 ( y1 y2 )1 3 a 3) (6)
2 y3 y4 y y 3 4 3
1 2 3 . y1 y2 y3 y4 are all real: y1 ab 6 c 2 a 3 27 2 2 3 12 y2 ( y1 (a 3 b) 27)
y3 ( a 1 ) 2 y4 ( y32 c 1 )1 2
(7)
Instead of cos1 ( ) with ( )2 when co mputing α, new parameter q can be defined as: 3
3
U U
q pi U i 2
i
i 1
i
* i
3
i 1
T11 SPAN
i
i 1
q has similar properties as α, and it only depends on T11 and SPAN. It can also describe the correlation between a coherency matrix and the surface scattering coherency matrix Ts wh ich rotation is invariant, so the random orientation caused by scattering echo randomness is not considered any more. Deorientation pre-process [9] can be neglected. Similar to formula (3), anisotropy A is: 3 (9) A 2 2 3 The correlation coefficient between an arbitrary T and Ts is given as follows: tr (TTs ) T11 T11 SPAN 1 R(T, T ) h q (10) s
tr (T2 ) tr (Ts2 )
tr (T2 ) SPAN
tr (T2 )
tr ( ) is the trace of a matrix. The definition of h is: h
SPAN 2
tr (T )
(11)
SPAN 3
3
T i 1 j 1
2
ij
h 1, 3 . Similar to H, h can also measure SAR target
random scattering properties while it has a one-to-one rela tionship with the depolarization index D[5]. According to dimensions of H/ , we can define the h/q plane shown as Fig.2.
3. New Approach As the stochastic fluctuation of scattering echo produce random orientation of the scattering goal easily, and to avoid the possible classificat ion error caused by the hypothesis of Freeman deco mposition, in this paper, we use h/q in in itial classification. Min imu m d istance measure and hierarchical cluster method are introduced for unsupervised classification. Pixels are filtered according to classification map in a sliding window. Details steps are as follows: (1) Perform h/q decomposition. (2) Unsupervised classification. a) Pixels are mapped to the h/q plane, forming 8 classes. To improve the classificat ion accuracy, compute the centre of each class, each pixel is classified again according to the minimum distance between the pixel and class centre. dmin min( T Vi ) (12) T is the coherency matrix. Vi is the mean value of the ith class pixel coherency matrix. b) For the 8 classes obtained in a), each class is divided into 2 subclusters bonding whether A is bigger than 0.5, forming 16 clusters. Revise classification by formula (12). c) For the new 16 clusters obtained in b), pixels in each cluster are sorted bonding their power and are divided into 3 clusters equally. Revise classification by formula (12). d) Agglomerative hierarchical clustering algorithm is introduced to merge similar clusters. The distance of the ith class and the jth class is: (13) 1 j 2, 2 m) Dm (Vi ,V j ) Vi V j ( i 1, m 1; m is the clusters number. Merge the two classes if their distance is minimu m. The new cluster is used for the next merging calcu lation. Final classification map fo rms when the number of clusters is achieved bonding the data used. (3) With the classificat ion map when non-point or curvelinear target pixel in a N N sliding window is filtered. a) Decide whether the centre p ixel in the N N window is a point or curve-linear target. If so, it will not be filtered. The decision method is: First, decide whether its value is the biggest in the window. If it is true, check the nu mber of pixels having the same class as centre pixel and the values are 0.95 times greater than the centre pixel’s in a 3 3 window. If the number is greater than a threshold TN, centre pixel is considered as a point or curve-linear target. b) Select the pixels taking part in filtering bonding the classification map. On ly the pixels which belong to the same class as centre pixel or its two neighbouring classes are chosen. If the number of selected pixels is less than n, pixels of the third neighbouring class are also selected. c) The selected pixels are weighted according to the distances between the pixels and the centre pixel. F iltering is done with the regulation of minimum mean square error: (14) T T b( b(T T) T is coherency matrix. T is the mean coherency matrix o f selected pixels. b [0 , 1] is the filtering coeffient. 4. Experiment Results AIRSA R L-band PolSA R data of Half moon bay is used in the experiment, it was orig inally sixteen-look processed. There are two airplanes in the scene, one is Cessna and the
other is Beechcraft; there is also a trihedral angle reflector. Image size is 250 400. Corresponding optical image and Pauli decomposition map are shown in Fig.3.
Fig.3. Optical image and Pauli decomposition map of Half moon bay area In the experiment, the number of final clusters is 27. Sliding window size is 9 9, and threshold n in pixels selection is 5, wh ich are the same as literature [5]. Threshold TN in point or curve-linear target judgment is 4. To demonstrate the validity of the proposed algorithm, we also show the experimental results of literature [5]. Orig inal and filtered images are shown in Fig.4, Fig.5 and Fig.6 respectively. 4.1 Effect on S peckle Reducti on and Texture Features Retaining To compare the filtered effect of the two algorith ms, we select eight parts fro m the filtered images of the three channels. They are respectively noted as A~H. Fro m the figures, we can see that in ocean area A, there are still some residual speckles in the result of literature [5], while the p roblem doesn’t exist in the results of new algorithm. In areas B C D E, the new algorith m can preserve all detail better; results of literature [5] are less clear. For linear
target shown in area F and point target shown in area G, literature [5] algorith m causes diffusion, and the new algorith m still has stronger abilit ies in processing these targets. In addition, the new algorith m is effective for the area whose gray level difference is small, such as H area. To illustrate the algorithm validity in speckle reduction more objectively, ENL (Equivalent Nu mber of Looks) of three areas which are ķocean, ĸgrassland, Ĺairport (see Fig.4) are calculated. The results are shown in Table 1. Table 1. ENL of the three areas. Original Literature[5] New image algorithm algorithm HH 12.44 170.49 276.82 Ocean HV 9.52 332.18 598.75 (area ķ) VV 12.75 114.60 412.42 HH 4.34 8.78 9.13 Grassland HV 0.92 1.49 1.77 (area ĸ ) VV 5.49 12.13 12.94 HH 3.37 3.42 3.75 Airport HV 4.39 6.61 13.96 (area Ĺ) VV 8.47 24.11 30.04 Table 1 shows that although the two algorith ms suppress speckle well, the new algorith m can obtain a higher ENL than that of literature [5]. It’s more effective not only in speckle reduction but also in preservation of structure characters. 4.2 The Preservation of Polarimetric Properties To evaluate the effect of polarimet ric properties preservation of filtered image, the fo llowing two parameters are [10] used :
m std .
1 M N Pf (i , j ) Po (i , j ) MN i 1 j 1
M N 1 ( Pf (i , j ) Po (i , j ) m) 2 ( MN 1) i 1 j 1
(15) (16)
P( , ) JTr KJ t 2 is the received power of antenna, J denotes Stokes vector. [ 4, 4] and [ 2, 2] denote the ellipticity and orientation angle respectively, and M, N are the sample nu mbers in their regions. Subscript f and o identify the original and filtered states. K is Kennaugh matrix. m is the mean distances between original received power and filtered ones. std . is the difference between m and the deviation of original and filtered received power. The s maller the values of the two parameters are, the better the preservation of polarimetric p roperties is. Different areas are selected to evaluate the filtered results, such as area ķ , ĸ , Ĺ in Fig.4 (a) which represents ocean, grassland and airport respectively. The areas including two planes are also selected (corresponding to Fig.3). Testing results are shown in Table 2 and Table 3 (COPOL is short for co-polarisation; CP is short for cross polarisation). Table 2. Comparison of m Literature [5] New algorithm m algorithm Ocean COPOL 0.0684 0.0691 (area ķ) CP 0.0408 0.0411 COPOL 0.1710 0.1568 Grassland CP 0.0987 0.0889 (area ĸ ) Airport COPOL 0.2192 0.2188 CP 0.1264 0.1249 (area Ĺ) COPOL 0.0799 0.0392 Beechcraft CP 0.0530 0.0354 COPOL 0.0730 0.0552 Cessna CP 0.0452 0.0430 Table 3. Comparison of std . Literature [5] std . New algorithm algorithm Ocean COPOL 0.0472 0.0477 (area ķ) CP 0.0268 0.0269 Grassland COPOL 0.1157 0.1046 CP 0.0635 0.0552 (area ĸ) Airport COPOL 0.1496 0.1444 (area Ĺ) CP 0.0769 0.0756 COPOL 0.0619 0.0256 Beechcraft CP 0.0349 0.0228 COPOL 0.0467 0.0383 Cessna CP 0.0292 0.0252 Fro m table 2 and table 3, we can see that the proposed algorith m has a similar effect on the polarimet ric p roperties preservation for ocean Compared with literature [5]; it behaves better performance for airport, grassland and the planes. It not only suppresses the speckle effectively, but also main tains the polarimetric properties better.
5. Conclusion Based on scattering model, th is paper develops an effecttive algorith m for speckle reduction by polarimetric decomposition and classification. As the new algorith m utilizes the
h/q method in initial classification, parameter derived fro m decomposition is rotation-invariance, wh ich can overcome the wrong classification caused by the random orientation for scattering echo randomness. Also, computing speed is faster, which can improve the image processing efficiency. For further classification, min imu m distance measure and hierarchical cluster method are introduced. Co mpared with the Wishart classifier used in Scattering-Model-Based speckle [5] filter , the proposed method is simp le, and it doesn’t involve inversion and trace of the matrix. In the filtering process, only the pixels that are not point or curve-linear targets are filtered, and the selected pixels are weighted according to the distances between their classes and centre pixel class to protect the polarimet ric properties better. Experimental results combing with AIRSA R L-band PolSA R data illustrate that the proposed algorith m is more effective not only in speckle reduction but also in polarimetric properties preservation. Acknowledgements This paper was supported by National Natural Science Foundation of China and Civil Aviat ion Administration of China (Item No. 60979002), Scientific Research Initial Foundation of Civil Aviat ion University of Ch ina (Item No. 2010QD03S) and Scientific Research Foundation of Civil Aviation University of Ch ina (Item No. 09CA UC_E10). The author would like to thank all teammates for the great effort. References [1] C. Jackson, H. Rais, et al. Polarimetry and Its Use in Automatic Target Detection with Examples fro m Search & Rescue. Proc.SPIE vol.3069, 1997: 204-214. [2] T. Zhang, P. Han, et al. Target Detection for Wrecked Plane Based on Yamaguchi Deco mposition[C]. 11th national radar annual meeting, Changsha, 2010. [3] L. M. Novak, et al. Optimal Speckle Reduction in Polarimetric SAR Imagery [J]. IEEE Trans. Aerosp. Electron. Syst., 1990, vol.26(3): 293-305. [4] J. S. Lee, et al. Speckle Reduction in Mult ipolarization, Multifrequency SAR Imagery [J]. IEEE Trans. on Geoscience and Remote Sensing, 1991, vol.29(4): 535-544. [5] J. S. Lee, et al. Scattering-Model-Based Speckle Filtering of Polarimetric SAR Data [J]. IEEE Trans. on Geoscience and Remote Sensing, 2006, vol.44(1):176-187. [6] W. T. An, Y. Cu i, et al. Fast Alternatives to H/a for Polarimetric SAR [J]. IEEE Trans. on Geoscience and Remote Sensing, 2010, vol.7(2):343-347. [7] F. Cao, et al. An Unsupervised Classification for Fully Polarimetric SA R Data Using Cloude-Pottler Deco mposition and Agglomerative Hierarchical Clustering Algorith m. Acta Electronica Signal, 2008, vol.36(3): 543-546. [8] S. Cloude, et al. A Review of Target Deco mposition Theorems in Radar Po larimetry[J]. IEEE Trans. on Geoscience and Remote Sensing, 1996, vol.34(2): 498518. [9] F. Xu, Y. Q. Jin, et al. Deorientation Theory of Polarime tric Scattering Targets and Application to Terrain Surface Classification [J]. IEEE Trans . on Geoscience and Remote Sensing, 2005, vol.43(10):2351-2364. [10] Q. Chen, Y. M. Jiang, et al. A Fast Speckle Filter-ing Based on Automatic Cecsoring for POLSA R Image [J], Signal Processing, 2010, 26(7): 1003-1009.
