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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. [ABSTRACT FROM AUTHOR]

With the improvements in modern radar resolution, the Gaussian-fluctuation model based on the central limit theorem does not accurately describe the scattering echo from targets. In contrast, the heavytailed Rayleigh distribution, based on the generalized central limit theorem, performs well in modeling the synthetic aperture radar (SAR) images, whereas its application to multi-look image processing is difficult. We describe successful modeling of multilook polarimetric SAR images with the heavy-tailed Rayleigh distribution and present novel parameter estimators based on matrix log-cumulants for the heavy-tailed Rayleigh distribution including the equivalent number of looks (ENL). First, a compound variable of heavy-tailed Rayleigh distribution is divided into a product of a positive alpha-stable variable and a complex Gaussian variable. The parameter estimations of the characteristic exponent and scale parameter based on log-cumulants in a single polarization channel are then derived. Second, the matrix log-cumulants (MLCs) for full polarization in multilook images are obtained, which can be applied to estimate model parameters. Therefore, a novel ENL estimator based on MLC is presented that describes the model more precisely. Extended to all other multivariable product models, this estimator performs better than existing methods. Finally, calculations on both simulated and real data are performed that give good fits with theoretical results. Multilook processing in one image with a fixed pixel number can improve parameter estimations over single-look processing. Our heavy-tailed Rayleigh model with its parameter estimation provides a new method to analyze the multilook polarimetric SAR images for target detection and classification. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multiple-tissue high-frequency skin ultrasound images. The distribution of multiple-tissue images is modeled as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. More precisely, a hybrid Metropolis-within-Gibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of in vivo skin tumors in high-frequency 2-D and 3-D ultrasound images. [ABSTRACT FROM PUBLISHER]

Synthetic aperture radar (SAR) imagery has found important applications due to its clear advantages over optical satellite imagery one of them being able to operate in various weather conditions. However, due to the physics of the radar imaging process, SAR images contain unwanted artifacts in the form of a granular look which is called speckle. The assumptions of the classical SAR image generation model lead to a Rayleigh distribution model for the histogram of the SAR image. However, some experimental data such as images of urban areas show impulsive characteristics that correspond to underlying heavy-tailed distributions, which are clearly non-Rayleigh. Some alternative distributions have been suggested such as the Weibull, log-normal, and the k-distribution which had success in varying degrees depending on the application. Recently, an alternative model namely the α-stable distribution has been suggested for modeling radar clutter. In this paper, we show that the amplitude distribution of the complex wave, the real and the imaginery components of which are assumed to be distributed by the α-stable distribution, is a generalization of the Rayleigh distribution. We demonstrate that the amplitude distribution is a mixture of Rayleighs as is the k-distribution in accordance with earlier work on modeling SAR images high showed that almost all successful SAR image models could be expressed as mixtures of Rayleighs. We also present parameter estimation techniques based on negative order moments for the new model. Finally, we test the performance of the model on urban images and compare with other models such as Rayleigh, Weibull, and the k-distribution. [ABSTRACT FROM AUTHOR]