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The performance analysis based on SAR sample covariance matrix.

Erten E - Sensors (Basel) (2012)

Bottom Line: Specifically, the maximum eigenvalue of the covariance matrix has been frequently used in different applications as target or change detection, estimation of the dominant scattering mechanism in polarimetric data, moving target indication, etc.In this paper, the statistical behavior of the maximum eigenvalue derived from the eigendecomposition of the sample multi-channel covariance matrix in terms of multi-channel SAR images is simplified for SAR community.Validation is performed against simulated data and examples of estimation and detection problems using the analytical expressions are as well given.

View Article: PubMed Central - PubMed

Affiliation: Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland. erten@ifu.baug.ethz.ch

ABSTRACT
Multi-channel systems appear in several fields of application in science. In the Synthetic Aperture Radar (SAR) context, multi-channel systems may refer to different domains, as multi-polarization, multi-interferometric or multi-temporal data, or even a combination of them. Due to the inherent speckle phenomenon present in SAR images, the statistical description of the data is almost mandatory for its utilization. The complex images acquired over natural media present in general zero-mean circular Gaussian characteristics. In this case, second order statistics as the multi-channel covariance matrix fully describe the data. For practical situations however, the covariance matrix has to be estimated using a limited number of samples, and this sample covariance matrix follow the complex Wishart distribution. In this context, the eigendecomposition of the multi-channel covariance matrix has been shown in different areas of high relevance regarding the physical properties of the imaged scene. Specifically, the maximum eigenvalue of the covariance matrix has been frequently used in different applications as target or change detection, estimation of the dominant scattering mechanism in polarimetric data, moving target indication, etc. In this paper, the statistical behavior of the maximum eigenvalue derived from the eigendecomposition of the sample multi-channel covariance matrix in terms of multi-channel SAR images is simplified for SAR community. Validation is performed against simulated data and examples of estimation and detection problems using the analytical expressions are as well given.

No MeSH data available.


(a) Comparison between the theoretical distributions and the histograms obtained from simulated data of the maximum sample eigenvalue. (b) The distribution of the maximum sample eigenvalue as a function of the number of samples, for a three-dimensional system. In both case, the powers are given by σk1 = σk2 = σk3 = 1 and correlations by ρk1k2 = 0, ρk1k3 = 0.8 and ρk2k3 = 0. When n → ∞, λmax = l1 = 1.8.
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f2-sensors-12-02766: (a) Comparison between the theoretical distributions and the histograms obtained from simulated data of the maximum sample eigenvalue. (b) The distribution of the maximum sample eigenvalue as a function of the number of samples, for a three-dimensional system. In both case, the powers are given by σk1 = σk2 = σk3 = 1 and correlations by ρk1k2 = 0, ρk1k3 = 0.8 and ρk2k3 = 0. When n → ∞, λmax = l1 = 1.8.

Mentions: Figure 2(a) shows the comparison of the Equation (4) with simulations. The theoretical PDF curves clearly agree with the histograms obtained from simulated data. As expected, the PDFs become narrower with increasing n, indicating less variance around the true value of the maximum eigenvalue l1 = 1.8. This behavior can be better seen in Figure 2(b) where the distribution of λmax as a function of the number of estimation samples n is presented. Note also that the expected value of the distributions seems to change for different n.


The performance analysis based on SAR sample covariance matrix.

Erten E - Sensors (Basel) (2012)

(a) Comparison between the theoretical distributions and the histograms obtained from simulated data of the maximum sample eigenvalue. (b) The distribution of the maximum sample eigenvalue as a function of the number of samples, for a three-dimensional system. In both case, the powers are given by σk1 = σk2 = σk3 = 1 and correlations by ρk1k2 = 0, ρk1k3 = 0.8 and ρk2k3 = 0. When n → ∞, λmax = l1 = 1.8.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3376554&req=5

f2-sensors-12-02766: (a) Comparison between the theoretical distributions and the histograms obtained from simulated data of the maximum sample eigenvalue. (b) The distribution of the maximum sample eigenvalue as a function of the number of samples, for a three-dimensional system. In both case, the powers are given by σk1 = σk2 = σk3 = 1 and correlations by ρk1k2 = 0, ρk1k3 = 0.8 and ρk2k3 = 0. When n → ∞, λmax = l1 = 1.8.
Mentions: Figure 2(a) shows the comparison of the Equation (4) with simulations. The theoretical PDF curves clearly agree with the histograms obtained from simulated data. As expected, the PDFs become narrower with increasing n, indicating less variance around the true value of the maximum eigenvalue l1 = 1.8. This behavior can be better seen in Figure 2(b) where the distribution of λmax as a function of the number of estimation samples n is presented. Note also that the expected value of the distributions seems to change for different n.

Bottom Line: Specifically, the maximum eigenvalue of the covariance matrix has been frequently used in different applications as target or change detection, estimation of the dominant scattering mechanism in polarimetric data, moving target indication, etc.In this paper, the statistical behavior of the maximum eigenvalue derived from the eigendecomposition of the sample multi-channel covariance matrix in terms of multi-channel SAR images is simplified for SAR community.Validation is performed against simulated data and examples of estimation and detection problems using the analytical expressions are as well given.

View Article: PubMed Central - PubMed

Affiliation: Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland. erten@ifu.baug.ethz.ch

ABSTRACT
Multi-channel systems appear in several fields of application in science. In the Synthetic Aperture Radar (SAR) context, multi-channel systems may refer to different domains, as multi-polarization, multi-interferometric or multi-temporal data, or even a combination of them. Due to the inherent speckle phenomenon present in SAR images, the statistical description of the data is almost mandatory for its utilization. The complex images acquired over natural media present in general zero-mean circular Gaussian characteristics. In this case, second order statistics as the multi-channel covariance matrix fully describe the data. For practical situations however, the covariance matrix has to be estimated using a limited number of samples, and this sample covariance matrix follow the complex Wishart distribution. In this context, the eigendecomposition of the multi-channel covariance matrix has been shown in different areas of high relevance regarding the physical properties of the imaged scene. Specifically, the maximum eigenvalue of the covariance matrix has been frequently used in different applications as target or change detection, estimation of the dominant scattering mechanism in polarimetric data, moving target indication, etc. In this paper, the statistical behavior of the maximum eigenvalue derived from the eigendecomposition of the sample multi-channel covariance matrix in terms of multi-channel SAR images is simplified for SAR community. Validation is performed against simulated data and examples of estimation and detection problems using the analytical expressions are as well given.

No MeSH data available.