With the development of polarimetric SAR system, such as the ALOS/PALSAR, the polarimetric observation shows great potential in many applications. As the models which describes the polarimetric property of the backscattering mechanism are based on the accurate acquisition of scattering matrix, so we have to restore the actual scattering matrix from the observed one. This is polarimetric calibration. If we want to quantitatively analyze polarimetric SAR data, polarimetric calibration is necessary and essential.
This is the polarimetric SAR model for calibration. The actual scattering matrix S describes the polarimetric backscattering property of targets. However, due to the existences of the system distortion and observation noise, the measured the scattering data can be presented by this distortion model. Here delta is the channel cross-talk, F is the channel imbalance, and N is the observation noise. So the objective of calibration is to restore the actual scattering matrix S from the observed data Z. As the noises are always neglected or reduced by averaging, we aim to estimate the system distortion parameter, delta and F. To estimate delta and F, some assumptions on the actual scattering matrices are utilized. Here we listed the most common 3. The first is the reciprocity on target. The second is the statistical symmetry, which leads to the un-correlation between co- and cross-polarization. And the third is using calibrators with known scattering matrices. Based on these assumptions, many researchers proposed different calibration methods.
However, there are still some remaining problems in polarimetric calibration. These are also the motivations of this research. The first problem is related to the Faraday rotation, which is a unique distortion effect for the low-frequency spaceborne SAR system. As the Faraday rotation is varying from time to time and from area to area, it is not included in many calibration procedure. Therefore we aim to investigate the Faraday rotation effect, and develop a method to estimate the Faraday rotation on the data after standard calibration. The second problem is, it is not so convenient to deploy the standard trihedral calibrators, especially for the low-frequency system. Moreover, the assumption that the co- and cross-polarizations are uncorrelated is based on the azimuth symmetry of the distributed target. But it is not always valid in many scenes. Therefore, we try to develop a calibration method without the trihedral or the un-correlation assumption. Alternatively, we will use some other assumptions instead. The third problem is, all the quantitative applications of polarimetric SAR data are assuming that the calibration is accurate enough. However, the absolute accurate calibration can not be guaranteed by anybody. Therefore we want to investigate if the calibration is not accurate enough, what is the impact, and we will take the soil moisture estimation as an example. These 3 items are the motivations and research contents in my thesis.
The proposed method follows the this procedure to estimate the system distortion parameters. Firstly the system distortion is decomposed into channel imbalance, non-reciprocal effect and reciprocal cross-talk. When estimating the channel imbalance, conventionally, the trihedral target is used. In our proposed method, we use the statistic information of the odd-bounce targets to substitute the trihedral. Then for the non-reciprocal effect, we use the similar method to the robust estimator of Faraday rotation, as the Faraday rotation is indeed a non-reciprocal effect. Finally, instead of the un-correlation assumption, we still need some other assumptions to estimate the remaining factor. Here we simply assume that the cross-talk is relatively small, to get the final results.
Here we show how the statistical information of the odd-bounce targets can be used as an alternative to the trihedral. We selected odd-bounce targets on the un-calibrated data by the following criteria: the diagonal elements should be with the same sign, the off-diagonal elements should be relatively small, and the backscattering intensity should be relatively large. These are some typical trihedral targets, we can found that the walls and ground from the similar structure to the trihedral. We estimated the channel imbalance product on these odd-bounce targets. We found that both the amplitude and the phase show prominent statistical distributions. We use the average of the amplitude and the peak of the phase to replace the information extracted from the trihedral.
Therefore we want to propose a robust estimator for the Faraday rotation on any scene. We found that the odd-bounce targets, which is the generalized type of trihedral, is good for the estimation of Faraday rotation. So we selected odd-bounce targets, and estimated Faraday rotation on these selected targets. We found that the histogram of the estimated Faraday rotation can be well approximated by the Laplace distribution, and we claim the maximum likelihood estimation of the location parameter mu in Laplace distribution as the robust estimation for Faraday rotation.
We compare the calibration result using the proposed method and provided by JAXA as follows. The distortion matrices estimated by the proposed method are very close to the JAXA distortion matrices, especially for the channel imbalance terms. The calibrated scattering matrix on the trihedral target also validates the effectiveness of the proposed methods. We found that the co-polarized signature on the trihedral target by the JAXA standard calibration and by the proposed method are very similar to each other, and both match the theoretical value well.
Polarimetric Calibration Using Distributed Odd-bounce Targets Jiong CHEN 1, 3* Motoyuki SATO 2 Jian YANG 3 1. Graduate School of Environmental Studies, Tohoku University, Japan 2. Center for Northeast Asian Studies, Tohoku University, Japan 3. Department of Electronic Engineering, Tsinghua University, China *E-mail: [email_address] 07/2011
After calibration Retrieval of soil moisture Estimation of biomass Classification of terrain Monitoring of flood ALOS/PALSAR Y. Oh 1992 H. Yamada, et.al. 2001 /13 Introduction
<ul><li>Polarimetric SAR Model for Calibration </li></ul><ul><li>Basic Assumptions </li></ul><ul><li>Conventional Methods </li></ul>/13 Polarimetric Calibration 1. Reciprocity 2.Statistical symmetry on distributed targets 3. Known Calibrators Van Zyl Quegan Kimura Assumption 1,2,3 Assumption 1,2 Assumption 1, Slight 2
<ul><li>The deployment of trihedral is inconvenient </li></ul><ul><ul><li>For low frequency system, the size should be relatively large </li></ul></ul><ul><ul><li>To implement calibration ubiquitously </li></ul></ul><ul><li>The assumption is not always valid </li></ul><ul><ul><li>Only valid for statistically symmetric distributed targets </li></ul></ul><ul><ul><li>Small value will cause large bias in the calibration results </li></ul></ul>Develop a calibration method without the trihedral or the assumption /13 Motivations
Conventional method : Trihedral Proposed method : Use the statistic information of odd-bounce targets Robust estimator using odd-bounce targets Assume cross-talk to be small /13 Basic Scheme and Assumptions Advantage : 1. Standard trihedral calibrator is not needed 2. The assumption is not needed
<ul><li>Statistical information of odd-bounce targets Trihedral </li></ul>/13 Typical odd-bounce targets Statistical property Amplitude Phase Flight direction Optical image, captured from Google Earth Selection of Odd-bounce Targets
<ul><li>Odd-bounce targets : Good for the estimation of </li></ul><ul><li>Distribution of on odd-bounce targets : Laplace </li></ul>/13 Similarity Parameters The robust estimate Fitting Result Laplace distribution with different parameters Robust Estimator of Non-reciprocal Effect
/13 On Odd-bounce targets Assuming Assuming Estimated Distortion Matrix Estimation of Cross-talk
<ul><li>Calibration result </li></ul>/13 New distortion matrices JAXA Standard distortion matrices Co-polarized signature on trihedral Uncalibrated JAXA standard calibrated result New calibrated result Theoretical result Discussion on Results
<ul><li>A practical calibration scheme based on distributed odd-bounce targets is proposed </li></ul><ul><ul><li>The distortion matrix is decomposed firstly </li></ul></ul><ul><ul><li>The statistical information of odd-bounce targets is used as alternative to trihedral </li></ul></ul><ul><ul><li>A robust estimator based on odd-bounce targets is derived to estimate the non-reciprocal effect </li></ul></ul><ul><ul><li>It can be used as a rough calibration method without the special deployment of trihedral calibrators, nor the un-correlation consumption </li></ul></ul>/13 Conclusion