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Statistics of phase difference and product magnitude of multi-look processed Gaussian signals. (English) Zbl 0809.60104

Summary: The phase difference and the product of two complex Gaussian signals are important parameters in the study of interferometry and polarimetry. To reduce statistical variations, polarimetric and interferometric radar systems adopt multi-look processing by averaging spatially in the complex interferogram. The statistical characteristics of these two parameters are different from those of the single-look processing. We derive their probability density functions (PDFs), and establish their statistical properties. These PDFs are derived from the complex Wishart distribution. The procedures involve multiple integrations of special functions, thus yielding closed-form, easily computable solutions for the PDFs. The multi-look phase difference has a Gauss hypergeometric distribution, and the multi-look product distribution is shown to be a product of two modified Bessel functions. Experimental results using polarimetric synthetic aperture radar data of forests indicate good agreement between computed histograms and theoretical distributions.

MSC:

60K40 Other physical applications of random processes
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
78A55 Technical applications of optics and electromagnetic theory
62M99 Inference from stochastic processes
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