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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 results for the third (skewness) and the fourth (kurtosis) order statistics of the sample maximum eigenvalue of a 2D system having powers σk1 = σk2 = 1 and correlations ρ = {0.2, 0.3, . . ., 0.9} versus the number of samples n = {2, 3, . . ., 62}.
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f4-sensors-12-02766: Theoretical results for the third (skewness) and the fourth (kurtosis) order statistics of the sample maximum eigenvalue of a 2D system having powers σk1 = σk2 = 1 and correlations ρ = {0.2, 0.3, . . ., 0.9} versus the number of samples n = {2, 3, . . ., 62}.

Mentions: The impact of the correlation and the number of samples on the behavior of the third (skewness) and fourth (kurtosis) order moment of the maximum sample eigenvalue λmax is presented in Figure 4. Skewness is a measure of how symmetrical the distribution is with respect to its mean. Figure 4(a,b) indicates that the skewness of λmax converges to zero for increasing n and increasing ρ, expressing the tendency to a symmetrical distribution in that cases.


The performance analysis based on SAR sample covariance matrix.

Erten E - Sensors (Basel) (2012)

Theoretical results for the third (skewness) and the fourth (kurtosis) order statistics of the sample maximum eigenvalue of a 2D system having powers σk1 = σk2 = 1 and correlations ρ = {0.2, 0.3, . . ., 0.9} versus the number of samples n = {2, 3, . . ., 62}.
© Copyright Policy
Related In: Results  -  Collection

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

f4-sensors-12-02766: Theoretical results for the third (skewness) and the fourth (kurtosis) order statistics of the sample maximum eigenvalue of a 2D system having powers σk1 = σk2 = 1 and correlations ρ = {0.2, 0.3, . . ., 0.9} versus the number of samples n = {2, 3, . . ., 62}.
Mentions: The impact of the correlation and the number of samples on the behavior of the third (skewness) and fourth (kurtosis) order moment of the maximum sample eigenvalue λmax is presented in Figure 4. Skewness is a measure of how symmetrical the distribution is with respect to its mean. Figure 4(a,b) indicates that the skewness of λmax converges to zero for increasing n and increasing ρ, expressing the tendency to a symmetrical distribution in that cases.

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.