Abstract
The span is widely employed in synthetic aperture radar (SAR) polarimetry (PolSAR) applications. The span is a summation of the three polarimetric intensity channels, its probability density function (pdf) is commonly assumed in the literature as that of the intensity polarimetric channel. In this letter, the statistics of the span are investigated. It has been demonstrated that the span is modeled by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> -looks intensity pdf where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> is the equivalent number of looks (ENLs) of the span transformation, i.e., ENL <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">span</sub> . To estimate ENL <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">span</sub> , a theoretical model has been proposed. The results showed that ENL <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">span</sub> ranges in [1,3] depending on the media’s scattering property. Results demonstrated also that the use of the eigenvalues produced better estimation of ENL <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">span</sub> than the use of diagonal elements of the coherence or the covariance matrix. The proposed model produced also a more accurate estimation of ENL <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">span</sub> than the one obtained by the direct calculation. Finally, it has been demonstrated that the use of the introduced span statistics gave a correct estimation of the performance of the classification and the filtering PolSAR techniques whereas classical span statistics overestimated them.
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