Topic
K-distribution
About: K-distribution is a research topic. Over the lifetime, 1281 publications have been published within this topic receiving 51774 citations.
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145 citations
08 Aug 1994
TL;DR: In this article, a K-distribution was developed to characterize the statistical properties of multi-look processed polarimetric SAR data, where the probability density function (PDF) was derived as the product of a gamma distributed random variable and the polarIMetric covariance matrix.
Abstract: A K-distribution has been developed to characterize the statistical properties of multi-look processed polarimetric SAR data. The probability density function (PDF) was derived as the product of a gamma distributed random variable and the polarimetric covariance matrix. The latter characterizes the speckle and the former depicts the inhomogeneity (texture). For multi-look data incoherently averaged from correlated one-look samples, the authors found that, for better modeling, the number of looks has to assume a non-integer value. A procedure was developed to estimate the equivalent number of looks and the parameter of the K-distribution. Experimental results using NASA/JPL 4-look and 16-1ook polarimetric SAR data substantiated this multi-look K-distribution. The authors also found that the multi-look process reduced the inhomogeneity and made the K-distribution less significant. >
145 citations
TL;DR: In this article, the trend to equilibrium of solutions to the spacehomogeneous Boltzmann equation for Maxwellian molecules with angular cutoff as well as with infinite-range forces is investigated. And the relation between several metrics for spaces of probability distributions, and the relation this to the Boltzman equation, by proving that Fourier-transformed solutions are at least as regular as the Fourier transform of the initial data, is established.
Abstract: This paper deals with the trend to equilibrium of solutions to the spacehomogeneous Boltzmann equation for Maxwellian molecules with angular cutoff as well as with infinite-range forces. The solutions are considered as densities of probability distributions. The Tanaka functional is a metric for the space of probability distributions, which has previously been used in connection with the Boltzmann equation. Our main result is that, if the initial distribution possesses moments of order 2+e, then the convergence to equilibrium in his metric is exponential in time. In the proof, we study the relation between several metrics for spaces of probability distributions, and relate this to the Boltzmann equation, by proving that the Fourier-transformed solutions are at least as regular as the Fourier transform of the initial data. This is also used to prove that even if the initial data only possess a second moment, then ∫∣v∣>R
f(v, t) ∣v∣2
dv→0 asR→∞, and this convergence is uniform in time.
143 citations
142 citations
TL;DR: In this article, random correlated ensembles of two quantum systems are investigated, including average entanglement entropies and probability distributions of Schmidt decomposition coefficients, and the reduced density operator distributions are compared with distributions induced via the Bures and Hilbert-Schmidt metrics.
140 citations