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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.


Detection performance of three different distributed scatterers using the PMF concept for different number of samples. (a) Azimuthal symmetric scatterer with ɛ = 1, γ = 0.5 and ρ = 0. (b) Reflection symmetric scatterer with ɛ = 1, γ = 0.8 and ρ = 0.8. (c) Reflection symmetric scatterer with ɛ = 0, γ = 0.8 and ρ = 0.8. The PFA is evaluated using the polarization independent clutter with ɛ = 1, γ = 1 and ρ = 0.
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f8-sensors-12-02766: Detection performance of three different distributed scatterers using the PMF concept for different number of samples. (a) Azimuthal symmetric scatterer with ɛ = 1, γ = 0.5 and ρ = 0. (b) Reflection symmetric scatterer with ɛ = 1, γ = 0.8 and ρ = 0.8. (c) Reflection symmetric scatterer with ɛ = 0, γ = 0.8 and ρ = 0.8. The PFA is evaluated using the polarization independent clutter with ɛ = 1, γ = 1 and ρ = 0.

Mentions: A three-dimensional polarimetric target detection problem was formulated making k = [SHHSHVSVV]T, where Si is the polarimetric scattering matrix element in channel i, and using the target covariance matrix structure(12)Σt=SHH[10ργ02ɛ0ρ*γ0γ].where , and ρ is the complex correlation coefficient between SHH and SVV [6,26]. Figure 8 shows the ROC curves for different number of samples for three different kinds of targets. Figure 8(a) corresponds to an azimuthal symmetric target having covariance matrix with parameters ɛ = 1, γ = 0.5 and ρ = 0. Figure 8(c) corresponds to a reflection symmetric target having covariance matrix with parameters ɛ = 1, γ = 0.8 and ρ = 0.8, while Figure 8(b) to a reflection symmetric target with parameters ɛ = 0, γ = 0.8 and ρ = 0.8 in its covariance matrix. For all three cases, SHH = 1 and the PFA was evaluated using the polarization independent clutter having ɛ = 1, γ = 1 and ρ = 0. Note that the curves vary not just with the number of used samples n but are also different for different targets having different Σt. This means that some types of targets are easier to detect than others, when using the quadratic detector described here and when the clutter is polarization independent. When the target covariance matrix is similar to the one of the clutter, the detection performance weakens (Figure 8(a)). On the other hand, when the covariance matrix of the target is significantly different from the clutter one, the detection performance improves (Figure 8(c)).


The performance analysis based on SAR sample covariance matrix.

Erten E - Sensors (Basel) (2012)

Detection performance of three different distributed scatterers using the PMF concept for different number of samples. (a) Azimuthal symmetric scatterer with ɛ = 1, γ = 0.5 and ρ = 0. (b) Reflection symmetric scatterer with ɛ = 1, γ = 0.8 and ρ = 0.8. (c) Reflection symmetric scatterer with ɛ = 0, γ = 0.8 and ρ = 0.8. The PFA is evaluated using the polarization independent clutter with ɛ = 1, γ = 1 and ρ = 0.
© Copyright Policy
Related In: Results  -  Collection

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

f8-sensors-12-02766: Detection performance of three different distributed scatterers using the PMF concept for different number of samples. (a) Azimuthal symmetric scatterer with ɛ = 1, γ = 0.5 and ρ = 0. (b) Reflection symmetric scatterer with ɛ = 1, γ = 0.8 and ρ = 0.8. (c) Reflection symmetric scatterer with ɛ = 0, γ = 0.8 and ρ = 0.8. The PFA is evaluated using the polarization independent clutter with ɛ = 1, γ = 1 and ρ = 0.
Mentions: A three-dimensional polarimetric target detection problem was formulated making k = [SHHSHVSVV]T, where Si is the polarimetric scattering matrix element in channel i, and using the target covariance matrix structure(12)Σt=SHH[10ργ02ɛ0ρ*γ0γ].where , and ρ is the complex correlation coefficient between SHH and SVV [6,26]. Figure 8 shows the ROC curves for different number of samples for three different kinds of targets. Figure 8(a) corresponds to an azimuthal symmetric target having covariance matrix with parameters ɛ = 1, γ = 0.5 and ρ = 0. Figure 8(c) corresponds to a reflection symmetric target having covariance matrix with parameters ɛ = 1, γ = 0.8 and ρ = 0.8, while Figure 8(b) to a reflection symmetric target with parameters ɛ = 0, γ = 0.8 and ρ = 0.8 in its covariance matrix. For all three cases, SHH = 1 and the PFA was evaluated using the polarization independent clutter having ɛ = 1, γ = 1 and ρ = 0. Note that the curves vary not just with the number of used samples n but are also different for different targets having different Σt. This means that some types of targets are easier to detect than others, when using the quadratic detector described here and when the clutter is polarization independent. When the target covariance matrix is similar to the one of the clutter, the detection performance weakens (Figure 8(a)). On the other hand, when the covariance matrix of the target is significantly different from the clutter one, the detection performance improves (Figure 8(c)).

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.