A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data

• Published in: IEEE transactions on geoscience and remote sensing Vol. 41; no. 1; pp. 4 - 19
• Main Authors: Conradsen, K., Nielsen, A.A., Schou, J., Skriver, H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2003; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied geophysics; Asymptotic properties; Backscattering; Change detection; Covariance matrix; Detectors; Earth sciences; Earth, ocean, space; Exact sciences and technology; Internal geophysics; L-band; Mathematical analysis; Pixels; Polarimetric synthetic aperture radar; Probability; Radar detection; Statistical analysis; Statistical distributions; Statistics; Synthetic aperture radar; Testing; Denmark; Scandinavia; Jutland; Western Europe; Europe; probability; remote sensing; near-field; covariance; Covariance matrix test statistic; backscattering; radar polarimetry; radar applications; remote sensing change detection; synthetic aperture radar; tests; imagery; polarization; Pixel; theory; EMISAR; statistics
• ISSN: 0196-2892; 1558-0644
• DOI: 10.1109/TGRS.2002.808066

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/spl times/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.