112 research outputs found
Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions
The scaled complex Wishart distribution is a widely used model for multilook
full polarimetric SAR data whose adequacy has been attested in the literature.
Classification, segmentation, and image analysis techniques which depend on
this model have been devised, and many of them employ some type of
dissimilarity measure. In this paper we derive analytic expressions for four
stochastic distances between relaxed scaled complex Wishart distributions in
their most general form and in important particular cases. Using these
distances, inequalities are obtained which lead to new ways of deriving the
Bartlett and revised Wishart distances. The expressiveness of the four analytic
distances is assessed with respect to the variation of parameters. Such
distances are then used for deriving new tests statistics, which are proved to
have asymptotic chi-square distribution. Adopting the test size as a comparison
criterion, a sensitivity study is performed by means of Monte Carlo experiments
suggesting that the Bhattacharyya statistic outperforms all the others. The
power of the tests is also assessed. Applications to actual data illustrate the
discrimination and homogeneity identification capabilities of these distances.Comment: Accepted for publication in the IEEE Transactions on Geoscience and
Remote Sensing journa
A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data
Abstract—When working with multilook fully polarimetric synthetic aperture radar (SAR) data, an appropriate way of representing the backscattered signal consists of the so-called covariance matrix. For each pixel, this is a 3 3 Hermitian positive definite matrix that follows a complex Wishart distribution. Based on this distribution, a test statistic for equality of two such matrices and an associated asymptotic probability for obtaining a smaller value of the test statistic are derived and applied successfully to change detection in polarimetric SAR data. In a case study, EMISAR L-band data from April 17, 1998 and May 20, 1998 covering agricultural fields near Foulum, Denmark are used. Multilook full covariance matrix data, azimuthal symmetric data, covariance matrix diagonal-only data, and horizontal–horizontal (HH), vertical–vertical (VV), or horizontal–vertical (HV) data alone can be used. If applied to HH, VV, or HV data alone, the derived test statistic reduces to the well-known gamma likelihood-ratio test statistic. The derived test statistic and the associated significance value can be applied as a line or edge detector in fully polarimetric SAR data also. Index Terms—Covariance matrix test statistic, EMISAR, radar applications, radar polarimetry, remote sensing change detection. I
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