Novel Target Decomposition Method based on Polarimetric Signatures Yilun Chen, Jian Yang Department of Electronic Engineering, Tsinghua University Beijing, 100084, P.R.China [email protected]

Abstract—Polarimetric signatures have been used successfully to present the scattering characteristics of a wide range of target types. However, most of previous researchers tend to provide a qualitative description rather than a quantitative analysis. In this paper, we propose a mathematical framework for analyzing the polarimetric signatures. The inner product between two polarimetric signatures is first defined, which is proved to have a simple form from elements of the Kennaugh matrices. The distance measurements are then introduced to quantify the difference between two polarimetric signatures. All these parameters are shown to have a compact form which is convenient for calculation. Based on these parameters, a novel target decomposition method is proposed which divides the target into several typical scattering mechanisms. With the least square rule, the proposed decomposition method can be carried out by the constrained quadratic programming. By using polarimetric Synthetic Aperture Radar (SAR) data, we demonstrate that the signature based decomposition method’s ability to reflect the target’s scattering mechanism, such as the components of single- and doublebounce, which can be employed for weak target detection.

1. Introduction For target detection and target recognition in radar polarimetry, an important problem is how to analyze characteristics of a radar target. According to the features of some typical targets, Huynen [3] proposed a set of parameters for describing the symmetry, structure, torsion and helicity of a target. Krogager [4] decomposed a target into three components corresponding to a sphere, a diplane and a helix. Cloude and Pottier [5, 6] introduced the concept of entropy for target decomposition and classification. Yang et al. extracted characteristics of a target based on the similarity parameter between two scattering matrices, which is convenient for analyzing some characteristics of a target. In this paper, a new target decomposition method is proposed based on the analysis of target’s polarimetric signatures. Polarimetric signatures, first introduced by van Zyl [1], are an effective way to characterize the polarization properties of microwave backscatter. These signatures have been used successfully in the past to present the scattering characteristics of a wide range of target types [2]. The signatures are significant because they utilize full amplitude and phase information from targets, which display backscattered intensity as a function of the polarization state of the backscattered TEM wave. The concept of a polarization ellipse is useful to provide a geometric interpretation of the polarization state of each point in the signature. This ellipse may be described in terms of two angles [χ, ψ] : the angle χ gives the ellipticity, or “fullness” of the scatter, while ψ gives the orientation with respect to the horizontal. For the col-pol case, the polarimetric signature P (χ, ψ) is determined for any arbitrary polarization state by calculating the Kennaugh matrix [K] and the transmit-receive polarization vectors P (χ, ψ) = gT [K] g, T

(1)

where g = (1, cos 2χ cos 2ψ, cos 2χ sin 2ψ, sin 2χ) and T indicates the transpose. The cross-pol case may be realized by letting receive antenna ellipticity χ be the negative of the transmit antenna ellipticity and by letting the receive orientation angle ψ be orthogonal to that of the transmit antenna, i.e., ψ + 900 . The rest of this paper is organized as follows: in section 2, we provide quantitative descriptions to analyze the relation between two polarimetric signatures, including the concept of inner product as well as their distance measurement. Based on these descriptions, the polarimetric signature based decomposition method is proposed in section 3 and validated by using polarimetric synthetic aperture radar data in section 4. Conclusions are summarized in section 5.

2. Quantitative descriptions of two polarimetric signatures 2.1 The inner product of polarimetric signatures Here we take the col-pol case first, the inner product between two signatures is defined as −π/ −π/ Z 4 Z 2 P1 (χ, ψ) P2 (χ, ψ) dχdψ, h P1 (χ, ψ) , P2 (χ, ψ)ic =

(2)

−π/ −π/ 2 4 where P1 (χ, ψ) and P2 (χ, ψ) denote the col-pol polarimetric signatures of target 1 and target 2, respectively; the subscript c stands for the col-pol case. By substituting eq.(1) into eq.(2), we can prove that hP1 (χ, ψ) , P2 (χ, ψ)ic = qT1 Wc q2 .

(3)

Here q is defined as the target’s characteristic vector, which is composed of elements from the Kennaugh matrix [K] = (kij )i,j=0...3 : T

q = (k00 , k01 , k02 , k03 , k11 , k12 , k13 , k22 , k23 ) . The weighted matrix Wc is calculated  19/16 0  0 1/2   0 0   0 0   −9/32 0 Wc =   0 0   0 0   −9/32 0 0 0

(4)

to be 0 0 1/2 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0

−9/32 0 0 0 25/128 0 0 19/128 0

0 0 0 0 0 3/32 0 0 0

0 0 0 0 0 0 1/8 0 0

−9/32 0 0 0 19/128 0 0 25/128 0

0 0 0 0 0 0 0 0 1/8

       2 π .      

(5)

From eq.(3) one can see that the defined inner product of polarimetric signatures turns to be the weighted inner product of two vectors q1 and q2 , which provides a simple form for computation. Similar results can be obtained for cross-pol case, where we replace Wc by Wx in eq.(3)   3/16 0 0 0 −1/32 0 0 −1/32 0  0 0 0 0 0 0 0 0 0     0 0 0 0 0 0 0 0 0     0 0 0 0 0 0 0 0 0    2 π 0 19/128 0 (6) Wx =   −1/32 0 0 0 25/128 0   0  0 0 0 0 3/32 0 0 0    0  0 0 0 0 0 1/8 0 0    −1/32 0 0 0 19/128 0  0 25/128 0 0 0 0 0 0 0 0 0 1/8 obtaining hP1 (χ, ψ) , P2 (χ, ψ)ix = qT1 Wx q2 ,

(7)

where the subscript x denotes the cross-pol case. 2.2 The distance measurement of polarimetric signatures The distance measurement of two signatures is defined as −π/ −π/ Z 4 Z 2 2 (P1 (χ, ψ) − P2 (χ, ψ)) dχdψ. kP1 (χ, ψ) − P2 (χ, ψ)kc = −π/ −π/ 2 4

(8)

Expanding the right term in eq.(8), there is

kP1 (χ, ψ) − P2 (χ, ψ)kc = hP1 (χ, ψ) , P1 (χ, ψ)ic − 2 hP1 (χ, ψ) , P2 (χ, ψ)ic + hP2 (χ, ψ) , P2 (χ, ψ)ic

(9)

Based on the results of the inner product which has been derived, we obtain the quadratic form T

kP1 (χ, ψ) − P2 (χ, ψ)kc = (q1 − q2 ) Wc (q1 − q2 ) .

(10)

For the cross-pol case, we just replace Wc by Wx .

3. Polarimetric signature based target decomposition The problem of target decomposition is to find the combination of several typical scattering mechanisms to represent a given target. For the signature value stands for the received power, one can expect a target’s polarimetric signature to be decomposed as N typical scattering mechanisms with distributed scatters in a resolution cell:

P (χ, ψ) =

N X

ai Pi (χ, ψ),

(11)

i=1

where Pi (χ, ψ) denotes a specific scattering component’s signature, and ai is its corresponding coefficient which should be a non-negative value. Due to the presence of speckle noise, we obtain the component coefficients {ai }i=1...N by solving the following constrained least square problem min ||P (χ, ψ) −

N P i=1

s.t.

ai Pi (χ, ψ)||γ

(12)

ai ≥ 0, i = 1...N,

where γ = c or x, denoting the col-pol case or the cross-pol case, respectively. Eq.(12) can be proved to be equivalent to min 12 aT Ra − cT a s.t. a ≥ 0.

(13)

T

a is the unknown vector (a1 , a2 , ..., aN ) , R is a N × N matrix where Rij = hPi (χ, ψ) , Pj (χ, ψ)iγ , and T

c = (c1 , c2 , ..., cN ) is a N × 1 column vector where ci = hPi (χ, ψ) , P (χ, ψ)iγ , the subscript γ = c or x. Eq.(13) can be solved via the standard quadratic programming method [9]. Given the coefficients {ai }i=1...N , we define the normalized component coefficients {ri }i=1...N as ri =

ai , N P ai

i = 1, ..., N.

(14)

i=1

ri reflects the percentage of the i th scattering component’s contribution to the whole scattering mechanism. Since {ri }i=1...N are normalized, they are determined by the shape of the polarimetric signature (i.e., the scattering mechanism) rather than the absolute received scattering intensity. £ ¤ According to Huyen’s theory, one knows that K 0 denotes the Kennaugh matrix £ 0of ¤ a target in a special position, where the orientation angle of the target equals to zero. If [K] is known, K can be obtained [3], therefore polarimetric signatures with zero target’s orientation angle can also be obtained. In practice, we first ”shift” a polarimetric signature to the zero orientation angle and then apply the proposed decomposition method. In this way, the decomposition results are invariable with target’s orientation angle.

A

A B

B

(a)

(b)

(c)

(d)

Figure 1: The span image of NASA ARC with decomposition results. (a) The span image (b)r1 (c) r2 (d) r3 .

4. Experimental results A NASA/JPL AIRSAR L-band image of the NASA ARC is used to test the proposed target decomposition method. The span image is shown in Fig.(a). In this experiment, we use a plate, a diplane and a wire as three kinds of basic scattering mechanism. Their Kennaugh matrices are supposed to be [K1 ], [K2 ] and [K3 ], respectively, where   [K1 ] =  



1

 , 

1 1 −1

  [K2 ] =  



1

 , 

1 −1 1





0.5 0.5  0.5 0.5 [K3 ] =   0

 . 

(15)

0

The Kennaugh matrix of each pixel is first pre-processed to rotate the target’s orientation angle to zero and then applied with the proposed decomposition method, here we use the col-pol signatures. The normalized component results r1 - r3 are shown in Fig. 1(b) - Fig.1(d), respectively. From these figures we can find that r1 has large value in the sea region (region A), which hints the main scattering mechanism of sea region is singlebounce. For the man-made objects, r1 turns to be small value and r2 , r3 begin to rise up. For instance, the linear-structured targets on the sea (region B)tend to have larger value of r3 , i.e., the wire-like targets. If we zoom in region B in Fig.1, we can find some linear objects, as the arrow points out (Fig.1(b)). These objects are weak scatters which are not easy to observe from the power image (Fig.3(a)), however, they are more salient from the proposed signature based decomposition results. The dark line on the sea hints the possibility of man-made objects. The picture from optical satellite of this region is also shown in Fig.3(c), where we can see that these objects do exist. We also use other decomposition methods for comparison. The polarization entropy and alpha angle [5, 6] are shown in Fig.2(a) and Fig.2(b), respectively. Fig.2(c) and Fig.2(d) show the similarity parameter [8] of single- bounce and double- bounce. From the comparison, it can be seen that the signature based decomposition results’ potential to detect weak targets.

5. Conclusion A new target decomposition method is presented in this paper which is based on the quantitative analysis of polarimetric signatures. The inner product and the distance measurement of two signatures are defined and then shown to have a simple form for calculation. Based on these quantitative descriptions, the signature based target decomposition method is proposed, where a target’s signature is divided into components from several typical targets. The normalized component coefficients can be used to reflect the scattering mechanism of the given target. Experimental results demonstrate the proposed method’s potential to discover weak man-made scatters, which is an important problem for target detection.

(a)

(b)

(c)

(d)

Figure 2: (a)The polarization entropy H. (b)The alpha angle α. (c)The similarity parameter of single- bounce s1 . (d) The similarity parameter of double- bounce s2 .

(a)

(b)

(c)

Figure 3: The decomposition results of weak targets. (a) The span image. (b) The decomposition result r1 . (c) The ground truth (optical image from satellite).

Acknowledgment This work was supported by the National Important Fundamental Research Plan of China (2001CB309401) and by the Fundamental Research Foundation of Tsinghua University. REFERENCES

1. Van Zyl J. J. , “On the importance of polarization in radar scattering problems”, Ph.D. dissertation, California Institute of Technology, Pasadena, 1985. 2. Evans D. L., Farr T. G., Van Zyl J. J. and Zebker H. A., “Radar polarimetry: Analysis tools and applications”, IEEE Transaction on Geoscience and Remote Sensing, vol. 26, pp. 774-789, 1988. 3. Huynen J. R., “Phenomenological Theory of Radar Targets”, Ph. D. Dissertation, 1970 4. Krogager E., “A New Decomposition of the Radar Target Scattering Matrix”, Electron. Lett., 1990, 26(18): 1525-1526 5. Cloude S. R., Pottier E., “An entropy based classification scheme for land applications of polarimetric SAR”, IEEE Tans. on Geoscience and Remote Sensing, 1997, 35(1): 68-78 6. Cloude S. R., Pottier E., “A Review of Target Decomposition Theorems in Radar Polarimetry”, IEEE Trans. Geosci. Remote Sensing, 1996, 34(2): 498-518 7. Freeman A., Durden S. L., “A Three-Component Scattering Model for Polarimetric SAR Data”, IEEE Trans. Geosci. Remote Sensing, 1998, 36(3): 963-973 8. Yang J., Peng Y. N. and et al., “Similarity between two scattering matrices”, IEE Electron. Lett. 2001, vol.37, no.3, pp. 193-194. 9. Coleman T.F. and Li Y., “A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on some of the Variables,” SIAM Journal on Optimization, Vol. 6, Number 4, pp 1040-1058, 1996.

Novel Target Decomposition Method based on ...

California Institute of Technology, Pasadena, 1985. 2. Evans D. L., Farr T. G., Van Zyl J. J. and Zebker H. A., “Radar polarimetry: Analysis tools and applica-.

6MB Sizes 0 Downloads 240 Views

Recommend Documents

Novel Target Decomposition Method based on ...
(a) The span image (b)r1 (c) r2 (d) r3. 4. Experimental results. A NASA/JPL AIRSAR L-band image of the NASA ARC is used to test the proposed target decomposition method. The span image is shown in Fig.(a). In this experiment, we use a plate, a diplan

A Domain Decomposition Method based on the ...
Nov 1, 2007 - In this article a new approach is proposed for constructing a domain decomposition method based on the iterative operator splitting method.

Novel method based on video tracking system for ...
A novel method based on video tracking system for simultaneous measurement of kinematics and flow in the wake of a freely swimming fish is described.

2D Shape Decomposition Based on Combined ...
by recent studies in visual human perception discussing the importance of ..... IEEE Transactions on Pattern Analysis and Machine Intelligence 29 (2007) 449–.

Multi-objective Local Search Based on Decomposition
lated objectives, we analyze these policies with different Moea/d para- ..... rithm using decomposition and ant colony. IEEE Trans. Cyber. 43(6), 1845–1859.

2D Shape Decomposition Based on Combined ...
cognitive research, suggesting that the human visual system uses a part-based represen- tation to analyze and interpret the shapes of objects [1][2][3]. Partitioning schemes are .... A shape boundary is a vector of points B = {b1, .., bm}. An endpoin

Notes on Decomposition Methods - CiteSeerX
Feb 12, 2007 - Some recent reference on decomposition applied to networking problems ...... where di is the degree of net i, i.e., the number of subsystems ...

A Novel Palmprint Feature Processing Method Based ...
ditional structure information from the skeleton images. It extracts both .... tain degree. The general ... to construct a complete feature processing system. And we.

A Novel Palmprint Feature Processing Method Based ...
processing approaches to handle online/offline palmprint, ... vert the original image into skeleton image with image pro- cessing .... it store nothing. For the ...

Notes on Decomposition Methods - CiteSeerX
Feb 12, 2007 - matrix inversion lemma (see [BV04, App. C]). The core idea .... this trick is so simple that most people would not call it decomposition.) The basic ...

Notes on Decomposition Methods - CiteSeerX
Feb 12, 2007 - is adjacent to only two nodes, we call it a link. A link corresponds to a shared ..... exponential service time with rate cj. The conjugate of this ...

A NOVEL EVOLUTIONARY ALGORITHMS BASED ON NUMBER ...
Proceedings of the International Conference on Advanced Design and Manufacture. 8-10 January, 2006, Harbin, China. A NOVEL EVOLUTIONARY ...

A NOVEL EVOLUTIONARY ALGORITHMS BASED ON NUMBER ...
Fei Gao. Dep. of Mathematics, Wuhan University of Technology, 430070, P. R .China. E-mail: ... based on Number Theoretic Net for detecting global optimums of.

Survey-based Exchange Rate Decomposition ...
understanding the dynamics of the exchange rate change. The expectational error is assumed to be mean zero and uncorrelated with variables in the information set used to form exchange rate expectations in period t. To further delve into this expectat

A Data Hiding Method Based on Ramp Secret ...
into an alpha channel plane Some security measures are also proposed for protecting the security of the shares hidden in the ... tampered, if the authentication signal generated from the current block content does not match with share that extracted

Protecting sensitive knowledge based on clustering method in data ...
Protecting sensitive knowledge based on clustering method in data mining.pdf. Protecting sensitive knowledge based on clustering method in data mining.pdf.

A collocated isogeometric finite element method based on Gauss ...
Sep 22, 2016 - ... USA; Phone: +1 612 624-0063; Fax: +1 612 626-7750; E-mail: do- [email protected]. Preprint submitted to Computer Methods in Applied Mechanics and ... locking-free analysis of beams [9, 10] and plates [11, 12], ...

An Energy Expenditure Estimation Method Based on ...
Summary of the validation studies. ... needed and only heart beat data and personal background parameters (e.g. ... EE is easily accessible from HR data.

Object Tracking Based On Illumination Invariant Method and ... - IJRIT
IJRIT International Journal of Research in Information Technology, Volume 2, Issue 8, August 2014, Pg. 57-66 ... False background detection can be due to illumination variation. Intensity of ... This means that only the estimated state from the.

A Progressive Image Transmission Method based on Discrete ...
A Progressive Image Transmission Method based on Discrete Wavelet Transform (DWT).pdf. A Progressive Image Transmission Method based on Discrete ...

Object Tracking Based On Illumination Invariant Method and ... - IJRIT
ABSTRACT: In computer vision application, object detection is fundamental and .... been set and 10 RGB frames are at the output captured by laptop's webcam.

Target Enhancement Oriented Fusion Method using ...
Poisson reconstruction based fusion method for polarimetric SAR images. 2.1 The definition of local .... data processing, such as multi-frequency and etc.

A Novel Error-Correcting System Based on Product ... - IEEE Xplore
Sep 23, 2011 - with large changes in signal amplitude and large values of log-likelihood ratios ... Low-density parity check (LDPC) codes and Reed-Solomon.