Significance of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>K</mml:mi></mml:math>Distributions in Scattering Experiments

Jakeman, E.; Pusey, P. N.

doi:10.1103/physrevlett.40.546

Cited by 280 publications

(139 citation statements)

References 12 publications

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“…(13) This new class of distributions is a generalization of the K-distribution (N = 1) which is a known compound distribution with applications to, e.g., scattering in random media [17] and turbulence [6,18]. From the asymptotic expansion of the function G p,q m,n , with m = q = 0 and n = p = N + 1, one finds that the tail of the distribution in this case is given by a modified stretched exponential (14) where…”

Section: B Marginal Distributionsmentioning

confidence: 99%

Universality classes of fluctuation dynamics in hierarchical complex systems

et al. 2017

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A unified approach is proposed to describe the statistics of the short time dynamics of multiscale complex systems. The probability density function of the relevant time series (signal) is represented as a statistical superposition of a large time-scale distribution weighted by the distribution of certain internal variables that characterize the slowly changing background. The dynamics of the background is formulated as a hierarchical stochastic model whose form is derived from simple physical constraints, which in turn restrict the dynamics to only two possible classes. The probability distributions of both the signal and the background have simple representations in terms of Meijer G-functions. The two universality classes for the background dynamics manifest themselves in the signal distribution as two types of tails: power law and stretched exponential, respectively. A detailed analysis of empirical data from classical turbulence and financial markets shows excellent agreement with the theory.

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Section: B Marginal Distributionsmentioning

confidence: 99%

Universality classes of fluctuation dynamics in hierarchical complex systems

et al. 2017

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“…Although the log-normal distribution is one of the most widely used turbulence models, this PDF is only applicable for weak turbulence conditions. It was shown in [23]- [26] that the K-distributed turbulence model provides good agreement with experimental data in a variety of FSO experiments involving radiation scattered by strong turbulence. In a recent series of papers on scintillation theory [11], [27], Andrews et al introduced the modified Rytov theory and the Gamma-Gamma PDF was proposed as a tractable mathematical model for a wide range of atmospheric turbulence levels.…”

Section: Literature Reviewmentioning

confidence: 69%

Terrestrial Coherent Free-Space Optical Communication Systems

Niu¹,

Cheng²,

Holzman³

2012

Optical Communication

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“…The Rician distribution is another generalization of the Rayleigh distribution and describes the presence of many coherent scatterers. The last one, introduced by Jakeman [3], the homodyned K distribution, describes the presence of few coherent scatterers.…”

Section: Modeling Ultrasound Imagesmentioning

confidence: 99%

A Modified Total Variation Denoising Method in the Context of 3D Ultrasound Images

Ogier

Hellier

2004

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2004

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Abstract. Ultrasound volumes are corrupted by a multiplicative noise, the speckle, which makes high level analysis difficult. Within each resolution cell a number of elementary scatterers reflects the incident wave toward the sensor. This paper proposes a method of restoration based on variational principles adapted to ultrasound images statistics. The contribution of this paper is two-fold: we first derive a modified TV scheme to integrate the multiplicative nature of the ultrasound noise and we propose to tune the parameter λ automatically accordingly to the local noise distribution thanks to the kurtosis information. We present qualitative and quantitative results on various ultrasound volumes.

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Significance ofKDistributions in Scattering Experiments

Cited by 280 publications

References 12 publications

Universality classes of fluctuation dynamics in hierarchical complex systems

Universality classes of fluctuation dynamics in hierarchical complex systems

Terrestrial Coherent Free-Space Optical Communication Systems

A Modified Total Variation Denoising Method in the Context of 3D Ultrasound Images

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