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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.


Theoretical versus simulation results (a) for the first order statistics (mean), and (b) for the second order statistics (variance), of the sample maximum eigenvalue of a two-dimensional system with powers σk1 = σk2 = 1 and correlation ρk1k2 = 0.2.
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f3-sensors-12-02766: Theoretical versus simulation results (a) for the first order statistics (mean), and (b) for the second order statistics (variance), of the sample maximum eigenvalue of a two-dimensional system with powers σk1 = σk2 = 1 and correlation ρk1k2 = 0.2.

Mentions: Figure 3(a) shows the variation of the histogram mean as a function of n for a two-dimensional case with fix correlation ρ = 0.2. In Figure 3(a), the theoretical expected value of λmax has been also over plotted for comparison. The curves match well, which validates Theorem III. The same has been carried out for the second order moment, i.e., the variance of λmax, and is presented in Figure 3(b). The agreement between the theoretical variance of λmax and the variance of the simulated data can again be confirmed. Also, as already observed in Figure 2(a), the lower the number of samples n, the higher the variance of λmax.


The performance analysis based on SAR sample covariance matrix.

Erten E - Sensors (Basel) (2012)

Theoretical versus simulation results (a) for the first order statistics (mean), and (b) for the second order statistics (variance), of the sample maximum eigenvalue of a two-dimensional system with powers σk1 = σk2 = 1 and correlation ρk1k2 = 0.2.
© Copyright Policy
Related In: Results  -  Collection

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

f3-sensors-12-02766: Theoretical versus simulation results (a) for the first order statistics (mean), and (b) for the second order statistics (variance), of the sample maximum eigenvalue of a two-dimensional system with powers σk1 = σk2 = 1 and correlation ρk1k2 = 0.2.
Mentions: Figure 3(a) shows the variation of the histogram mean as a function of n for a two-dimensional case with fix correlation ρ = 0.2. In Figure 3(a), the theoretical expected value of λmax has been also over plotted for comparison. The curves match well, which validates Theorem III. The same has been carried out for the second order moment, i.e., the variance of λmax, and is presented in Figure 3(b). The agreement between the theoretical variance of λmax and the variance of the simulated data can again be confirmed. Also, as already observed in Figure 2(a), the lower the number of samples n, the higher the variance of λmax.

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.