Abstract
In this paper, a mixture of generalized Cauchy distribution and Rayleigh distribution that possesses a closed-form expression is proposed for modeling the heavy-tailed Rayleigh (HTR) distribution. This new approach is developed for analytically modeling the amplitude distribution of ultrasound images based on the HTR distribution. HTR as a non-Gaussian distribution is basically the amplitude probability density function (PDF) of the complex isotropic symmetric α-stable (S α S) distribution which appears in the envelope distribution of ultrasonic images. Analytic expression for HTR distribution is a momentous consideration in signal processing with stable random variables. Furthermore, we introduce a mixture ratio estimator based on the energy of amplitude PDF which contains both α and γ parameters. For a quantitative assessment, we compare the accuracy and computational complexity of the proposed mixture with other approximations of HTR distribution through several numeral simulations on synthetic random samples. Experimental results obtained from the Kolmogorov-Smirnov (K-S) distance and Kullback-Leibler (K-L) divergence as the goodness-of-fit tests on real ultrasound images reveal the favor of the new mixture model.
Highlights
In the medical context, ultrasound provides a noninvasive technique of imaging human anatomy with good visualization characteristics and relatively easy management [1]
We statistically model the envelope distribution of ultrasound images as a new generalized Cauchy-Rayleigh mixture approximation based on heavy-tailed Rayleigh (HTR)
Hereinafter, we focus on HTR distribution with 1 ≤ α ≤ 2, which is defined in terms of its characteristic function (CF), as the following: φα,γ (ω) = exp −γ |ω|α, (8)
Summary
Ultrasound provides a noninvasive technique of imaging human anatomy with good visualization characteristics and relatively easy management [1]. We statistically model the envelope distribution of ultrasound images as a new generalized Cauchy-Rayleigh mixture approximation based on HTR distribution. Analytical derivation for mixture ratio estimation based on the characteristic exponent parameter and the dispersion parameter of HTR distribution which has closed-form expression is derived. The PDF characterized by (9) is demonstrated as an empirical model which is ideal for modeling ultrasound amplitude RF returns The reason for this appellation is that this new generalized form of the Rayleigh distribution can illustrate impulsive behavior and has heavier tails rather than the classical Rayleigh distribution. The main disadvantage of these methods is the utilization of SαS mixture ratio for HTR distribution, whereas the HTR distribution is the amplitude PDF of a complex SαS random variable and is not symmetric. We propose our model for amplitude PDF of ultrasound images based on a mixture approximation of HTR distribution
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