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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.


Maximum sample eigenvalue detection performance as a function of the number or channels m, samples n and correlation ρ. (a) ROC curves for different multidimensional systems, m = {2, 3, 6} and n = 6. (b) ROC curves for the two- and three-dimensional cases, and for different number of samples n. (c) ROC curves for the two-dimensional case, n = 3, and for different correlation.
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f7-sensors-12-02766: Maximum sample eigenvalue detection performance as a function of the number or channels m, samples n and correlation ρ. (a) ROC curves for different multidimensional systems, m = {2, 3, 6} and n = 6. (b) ROC curves for the two- and three-dimensional cases, and for different number of samples n. (c) ROC curves for the two-dimensional case, n = 3, and for different correlation.

Mentions: Figure 7(a) shows the detection performance as a function of the dimension of the multichannel system, i.e., m = 2, e.g., interferometric, m = 3, e.g., polarimetric and m = 6, e.g., polarimetric-interferometric system. For all cases, with fixed number of samples n = 6, one can realize that the performance of detection is significantly improved as the number of SAR images increases. Figure 7(b) shows the ROC curves for m = {2, 3} and for different number of samples n. It can be seen that for both multidimensional system configurations the number of samples increases the detection performance.


The performance analysis based on SAR sample covariance matrix.

Erten E - Sensors (Basel) (2012)

Maximum sample eigenvalue detection performance as a function of the number or channels m, samples n and correlation ρ. (a) ROC curves for different multidimensional systems, m = {2, 3, 6} and n = 6. (b) ROC curves for the two- and three-dimensional cases, and for different number of samples n. (c) ROC curves for the two-dimensional case, n = 3, and for different correlation.
© Copyright Policy
Related In: Results  -  Collection

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

f7-sensors-12-02766: Maximum sample eigenvalue detection performance as a function of the number or channels m, samples n and correlation ρ. (a) ROC curves for different multidimensional systems, m = {2, 3, 6} and n = 6. (b) ROC curves for the two- and three-dimensional cases, and for different number of samples n. (c) ROC curves for the two-dimensional case, n = 3, and for different correlation.
Mentions: Figure 7(a) shows the detection performance as a function of the dimension of the multichannel system, i.e., m = 2, e.g., interferometric, m = 3, e.g., polarimetric and m = 6, e.g., polarimetric-interferometric system. For all cases, with fixed number of samples n = 6, one can realize that the performance of detection is significantly improved as the number of SAR images increases. Figure 7(b) shows the ROC curves for m = {2, 3} and for different number of samples n. It can be seen that for both multidimensional system configurations the number of samples increases the detection performance.

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.