Showing papers on "K-distribution published in 2006"
TL;DR: Experimental studies show that the RiIG MAP filter has excellent filtering performance in the sense that it smooths homogeneous regions, and at the same time preserves details.
Abstract: In this paper, a new statistical model for representing the amplitude statistics of ultrasonic images is presented. The model is called the Rician inverse Gaussian (RiIG) distribution, due to the fact that it is constructed as a mixture of the Rice distribution and the Inverse Gaussian distribution. The probability density function (pdf) of the RiIG model is given in closed form as a function of three parameters. Some theoretical background on this new model is discussed, and an iterative algorithm for estimating its parameters from data is given. Then, the appropriateness of the RiIG distribution as a model for the amplitude statistics of medical ultrasound images is experimentally studied. It is shown that the new distribution can fit to the various shapes of local histograms of linearly scaled ultrasound data better than existing models. A log-likelihood cross-validation comparison of the predictive performance of the RiIG, the K, and the generalized Nakagami models turns out in favor of the new model. Furthermore, a maximum a posteriori (MAP) filter is developed based on the RiIG distribution. Experimental studies show that the RiIG MAP filter has excellent filtering performance in the sense that it smooths homogeneous regions, and at the same time preserves details.
120 citations
01 Jul 2006
TL;DR: In this article, the spatial distribution of X-band, high-resolution and high grazing angle polarimetric sea clutter data is studied and the KK and WW distribution models are proposed to fit the distribution of sea clutter with spikes.
Abstract: : This report studies the spatial distribution of X-band, high resolution and high grazing angle polarimetric sea clutter data. The K distribution usually provides a good fit for the distribution of the VV polarised data. The HH polarised data is spikiest and its distribution exhibits a sudden departure from the K distribution in the tail region, which usually requires the KA or the similar distributions to achieve a better fit in the tail region. Due to drawbacks of the KA distribution, this report proposes the KK and WW distribution models to fit the distribution of sea clutter with spikes. It is found that the KK distribution provides overall the best fit. Distributions of the sum of K and Weibull distributed samples are also presented.
94 citations
TL;DR: In this article, a new family of distributions for non-negative data, defined by means of a quantile function, is introduced, which is applied to an example from environmental engineering.
Abstract: We introduce a new, flexible family of distributions for non-negative data, defined by means of a quantile function. We describe some properties of this family, and discuss several methods for estimating the parameters. The distribution is applied to an example from environmental engineering.
91 citations
Patent•
07 Jul 2006TL;DR: In this article, an expectation-maximization procedure is applied iteratively to the probability distribution to determine components of the probability distributions, and a method decomposes input data acquired of a signal.
Abstract: A method decomposes input data acquired of a signal. An input signal is sampled to acquire input data. The input data is represented as a probability distribution. An expectation-maximization procedure is applied iteratively to the probability distribution to determine components of the probability distributions.
59 citations
TL;DR: The statistics of the radio frequency signal in the case of partially developed speckle are studied using the K distribution framework and the ability of the proposed distribution to model RF echographic signals from cardiac tissues is evaluated from data acquired in vivo.
Abstract: We study in this paper the statistics of the radio frequency (RF) signal in the case of partially developed speckle. Using the K distribution framework, we give the probability density function of the associated distribution, the corresponding moments, and estimators for the parameters of the distribution. The consistency of the proposed estimators is evaluated in terms of their bias and variance through numerical simulations. The ability of the proposed distribution to model RF echographic signals from cardiac tissues is evaluated from data acquired in vivo
37 citations
01 Jan 2006
TL;DR: In this article, the univariate and multivariate generalisations of the following distributions: the Birnbaum-Saunders, the three parameter BSS, and the sinh-normal of spherical type were proposed, when the stochastic representation of a spherical random vector is assumed.
Abstract: This work proposes the univariate and multivariate generalisations of the following distributions: the Birnbaum-Saunders, the three parameter Birnbaum-Saunders and the sinh-normal of spherical type. Similarly, when the stochastic representation of a spherical random vector is assumed, we propose alternative definitions for the above-mentioned distributions including the log-elliptical distribution. We emphasize that all the distributions here derived belong to the family of the spherical distributions. Mathematics Subject Classification: 62E15, 62N05
36 citations
Journal Article•
TL;DR: A new dynamic Interpolation Search data structure is presented that achieves O(loglogn) search time with high probability on unknown continuous or even discrete input distributions with measurable probability of key collisions, including power law and Binomial distributions.
Abstract: A new dynamic Interpolation Search (IS) data structure is presented that achieves O(loglogn) search time with high probability on unknown continuous or even discrete input distributions with measurable probability of key collisions, including power law and Binomial distributions. No such previous result holds for IS when the probability of key collisions is measurable. Moreover, our data structure exhibits 0(1) expected search time with high probability for a wide class of input distributions that contains all those for which o(log log n) expected search time was previously known.
33 citations
TL;DR: In this paper, the authors obtain two new distributions in frequency probability theory and demonstrate them in particular in the example of frequency dictionaries, one of which gives a logarithmic correction to the Zipf-Mandelbrot law, and the other describes the "tails" of the distribution.
Abstract: We obtain two new distributions in frequency probability theory and demonstrate them, in particular, in the example of frequency dictionaries. One of these distributions gives a logarithmic correction to the Zipf-Mandelbrot law, and the other describes the “tails” of the distribution.
28 citations
TL;DR: In this article, the exact expression for the convolution of gamma distributions with different scale parameters is quite complicated, and the approximation by means of another gamma distribution is shown to be remarkably accurate for wide ranges of the parameter values, in particular if more than two variables are involved.
Abstract: The exact expression for the convolution of gamma distributions with different scale parameters is quite complicated. The approximation by means of another gamma distribution is shown to be remarkably accurate for wide ranges of the parameter values, in particular if more than two variables are involved.
27 citations
01 Sep 2006
TL;DR: In this paper, the authors measured the narrowband envelope amplitude distributions from the TREX04 data (as a function of frequency) using M-sequence signals centered at 17 kHz with a 5 kHz bandwidth.
Abstract: In a fading channel, bit error rate for frequency-shift-keying keyingsignals is determined predominantly by the envelope amplitude fading statistics of the signal. The narrowband envelope amplitude distributions are measured from the TREX04 data (as a function of frequency) using M-sequence signals centered at 17 kHz with a 5 kHz bandwidth. The results do not fit the Rayleigh, Rician, Nakagami rn-distributions. In contrast, we find that the data are fitted well by a K-distribution. We also analyze the data in terms of long-term and short-term statistics. The long-term and short-term fading statistics are well fitted by the lognormal distribution and Rayleigh distribution respectively, choosing the average time scale to be ~ 0.2 sec. The joint probability distribution function of a lognormal and the Rayleigh distribution is approximately the R-distribution.
TL;DR: In this article, it was shown that any scale mixture of normal distributions is always a term of a sequence of elliptical distributions, increasing in dimension, and that all the terms of this sequence are also scale mixtures of normal distribution sharing the same mixing distribution function.
TL;DR: In this article, the authors measure fidelity of a single-rou asymmetric communication protocol by the relative entropy, which is the probability that the client will send more bits than the server wants to send.
TL;DR: The order parameter of the K-distribution can be a promising new parameter to estimate the forest biomass from high-resolution polarimetric SAR data in a much wider range than the conventional RCS method.
Abstract: The purpose of this letter is to present the results on the study of searching effective parameters that describe the relation between high-resolution synthetic aperture radar (SAR) images and forest parameters The study is based on the non-Gaussian texture analysis of the polarimetric airborne Pi-SAR data over coniferous forests in Hokkaido, Japan The radar cross section (RCS) in terms of a forest biomass is first analyzed It is found that the L-band RCS increases steadily with the biomass and saturates at approximately 40 tons/ha These results are similar to the previous studies The probability density function of the image amplitude is then investigated, and among Rayleigh, log-normal, Weibull, and K-distributions, the K-distribution is found to fit best to the L-band data of all polarizations, although the Weibull distribution fits equally well Further, the correlation between the tree biomass and the order parameter of the K-distribution in the cross-polarization images is found to be very high, and the order parameter increases consistently with the biomass to approximately 100 tons/ha, which is well beyond the saturation limit of the L-band RCS Thus, the order parameter of the K-distribution can be a promising new parameter to estimate the forest biomass from high-resolution polarimetric SAR data in a much wider range than the conventional RCS method
TL;DR: The goodness-of-fit tests for two and three-parameter gamma distributions are based on minimum quadratic forms of standardized logarithmic differences of values of the moment generating function and its empirical counterpart as mentioned in this paper.
Abstract: This article presents goodness-of-fit tests for two and three-parameter gamma distributions that are based on minimum quadratic forms of standardized logarithmic differences of values of the moment generating function and its empirical counterpart. The test statistics can be computed without reliance to special functions and have asymptotic chi-squared distributions. Monte Carlo simulations are used to compare the proposed test for the two-parameter gamma distribution with goodness-of-fit tests employing empirical distribution function or spacing statistics. Two data sets are used to illustrate the various tests.
18 Sep 2006
TL;DR: An algorithm for learning Kikuchi approximations from data based on the expectation-maximization (EM) paradigm is presented and the proposal is tested in the approximation of probability distributions that arise in evolutionary computation.
Abstract: Mixtures of distributions concern modeling a probability distribution by a weighted sum of other distributions. Kikuchi approximations of probability distributions follow an approach to approximate the free energy of statistical systems. In this paper, we introduce the mixture of Kikuchi approximations as a probability model. We present an algorithm for learning Kikuchi approximations from data based on the expectation-maximization (EM) paradigm. The proposal is tested in the approximation of probability distributions that arise in evolutionary computation.
TL;DR: In this article, the exact distribution of $P = X Y$ and the corresponding moment properties are derived when the random vector $(X, Y)$ has two of the most flexible bivariate gamma distributions.
Abstract: Bivariate and univariate gamma distributions are some of the most popular models for hydrological processes. In fact, the intensity and the duration of most hydrological variables are frequently modeled by gamma distributions. This raises the important question: what is the distribution of the total amount = intensity $\times$ duration? In this paper, the exact distribution of $P = X Y$ and the corresponding moment properties are derived when the random vector $(X, Y)$ has two of the most flexible bivariate gamma distributions. The expressions turn out to involve several special functions.
Journal Article•
TL;DR: In this paper, the authors introduce the mixture of Kikuchi approximations as a probability model, which is tested in the approximation of probability distributions that arise in evolutionary computation, and they present an algorithm for learning Kikuchi approximation from data based on the expectationmaximization (EM) paradigm.
Abstract: Mixtures of distributions concern modeling a probability distribution by a weighted sum of other distributions. Kikuchi approximations of probability distributions follow an approach to approximate the free energy of statistical systems. In this paper, we introduce the mixture of Kikuchi approximations as a probability model. We present an algorithm for learning Kikuchi approximations from data based on the expectation-maximization (EM) paradigm. The proposal is tested in the approximation of probability distributions that arise in evolutionary computation.
06 Apr 2006
TL;DR: The ability of the proposed distribution to model RD echocardiographic signals from cardiac tissue and blood region is demonstrated on data acquired in vivo.
Abstract: We study in this work the statistics of the radio frequency (RF) signal for both fully and partially developed speckle in echocardiographic images in the context of image segmentation and classification. From physical image formation model, we first derive the probability density function (PDF) of the RF signal using the K distribution framework. We then show that this pdf may be reliably approximated through a generalized Gaussian distribution. The ability of the proposed distribution to model RD echocardiographic signals from cardiac tissue and blood region is demonstrated on data acquired in vivo.
01 Oct 2006
TL;DR: In this article, generalized gamma (GG) distribution is used to estimate the noise characteristics of a synthetic aperture radar (SAR) image, and the major parameter of the GG distribution is estimated according to the maximum likelihood (ML) principle.
Abstract: Speckle noise is an inherent property of a synthetic aperture radar (SAR) image, and it generally tends to reduce the image resolution and contrast. The speckle noise estimation is an important prerequisite, whenever SAR image is used for object segmentation. Among the many methods in statistical description that have been proposed to perform the estimation, there exists a class of approaches that use a multiplicative model of speckled image formation, such as Rayleigh distribution, K-distribution, Weibull distribution etc. In this paper, generalized gamma (GG) distribution is used to estimate the noise characteristics. GG distribution is especially attractive because it contains several distributions as special cases, viz. Rayleigh, exponential, Weibull, and log-normal. The major parameter of the GG distribution is estimated according to maximum likelihood (ML) principle. The proposed method works successfully when the solution is located in the parameter space. For verifying the performance of the proposed scheme compared to the other methods, we use a ?2 goodness-of-fit (GOF) test.
23 May 2006
TL;DR: In this paper, the sensitivity of the generalized K-distribution as descriptors of dark features over marine single-look SAR images is investigated, and the working hypothesis is that the generalized k-dist distribution is a suitable speckle model for marine SAR images ensuring a continuous and physically consistent transition among different scattering scenarios.
Abstract: In this paper, the sensitivity of the three parameters generalized K-distribution, as descriptors of dark features over marine single-look SAR images, is investigated. The working hypothesis is that the generalized K-distribution, which is a three parameters probability density function (pdf), is a suitable speckle model for marine SAR images ensuring a continuous and physically consistent transition among different scattering scenarios. This speckle model can embody the Rayleigh case (which is descriptor of land areas, i.e. islands), the Rice case (which is descriptor of areas in which is present a dominant scatterer, i.e. ships) and the K distribution (which is descriptor of oil free areas). The reference data set is provided by the ESA under the CAT-1 Project C1P-2769.
10 Jul 2006
TL;DR: In this paper, a new dynamic interpolation search (IS) data structure is presented that achieves O(loglogn) search time with high probability on unknown continuous or even discrete input distributions with measurable probability of key collisions, including power law and Binomial distributions.
Abstract: A new dynamic Interpolation Search (IS) data structure is presented that achieves O(loglogn) search time with high probability on unknown continuous or even discrete input distributions with measurable probability of key collisions, including power law and Binomial distributions. No such previous result holds for IS when the probability of key collisions is measurable. Moreover, our data structure exhibits O(1) expected search time with high probability for a wide class of input distributions that contains all those for which o(loglogn) expected search time was previously known.
07 Jun 2006
TL;DR: The three K distributions are shown to be statistical models for the amplitude signals, corresponding to special cases of this generic model, and new iterative algorithms for estimating the parameters associated with each model are presented.
Abstract: In this paper we re-derive the probability density functions (pdfs) of the K distribution, the homodyned K distribution, and the generalized K distribution in the framework of scale mixture of Gaussians models. This is done by considering the complex envelope corresponding to a received signal as a double stochastic circular Gaussian variable, in which both the variance and the mean are linearly scaled by a stochastic factor Z. By assuming Z to be ? distributed, the three K distributions are shown to be statistical models for the amplitude signals, corresponding to special cases of this generic model. We also present new iterative algorithms for estimating the parameters associated with each model.
TL;DR: In this article, the exact distributions of R = X +Y and W = X/(X +Y ) and corresponding moment properties are derived when X and Y follow five flexible bivariate gamma distributions.
Abstract: Exact distributions of R = X +Y and W = X/(X +Y ) and the corresponding moment properties are derived when X and Y follow five flexible bivariate gamma distributions. The expressions turn out to involve several special functions.
TL;DR: In this paper, the joint probability distribution of number of 0-runs and number of 1-runs of length in n trials is studied. And the main tool used to obtain the probability generating function of the joint distribution is the conditional probability generating functions method.
Abstract: Consider a time homogeneous {0, 1}-valued m-dependent Markov chain \(\{X_{- m + 1 + n}, n \geqslant 0\}\). In this paper, we study the joint probability distribution of number of 0-runs of length \(k_{0} (k_{0} \geqslant m)\) and number of 1-runs of length \(k_{1} (k_{1} \geqslant m)\) in n trials. We study the joint distributions based on five popular counting schemes of runs. The main tool used to obtain the probability generating function of the joint distribution is the conditional probability generating function method. Further a compact method for the evaluation of exact joint distribution is developed. For higher-order two-state Markov chain, these joint distributions are new in the literature of distributions of run statistics. We use these distributions to derive some waiting time distributions.
01 Jan 2006
TL;DR: In this article, second order probability density functions are used to investigate logical argument forms and the conclusions are mixtures of beta distributions, where the shape parameters of the distributions are assumed to be additive (natural sampling).
Abstract: Logical argument forms are investigated by second order probability density functions. When the premises are expressed by beta distributions, the conclusions usually are mixtures of beta distributions. If the shape parameters of the distributions are assumed to be additive (natural sampling), then the lower and upper bounds of the mixing distributions (P olya-Eggenberger distributions) are parallel to the corresponding lower and upper probabilities in conditional probability logic.
TL;DR: In this article, the Akaike Information Criterion (AIC) was introduced to determine the weather clutter amplitude, which is more rigorous fit of the distribution to the data than the least squares method.
Abstract: We observed weather clutter from rain clouds using an L-band long-range air-route surveillance radar (ARSR) having a frequency 1.3 GHz, a beamwidth 1.2°, and a pulsewidth 3.0 μs. To determine the weather clutter amplitude, we introduce the Akaike Information Criterion (AIC), which is more rigorous fit of the distribution to the data than the least squares method. It is discovered that the weather clutter amplitudes obey almost the Rayleigh distribution for entire data and the Weibull, log-Weibull, and K-distributions with the shape parameters of 1.73 to 2.43, 10.60, and 5.13 to 50.93, respectively, for data within the beam width of an antenna.
TL;DR: This paper used pieces of thermodynamics' first law to generate probability distributions for generalized ensembles when only level-population changes are involved, which can be associated not exclusively to heat and acquire a more general meaning.
Abstract: We show here how to use pieces of thermodynamics’ first law to generate probability distributions for generalized ensembles when only level-population changes are involved. Such microstate occupation modifications, if properly constrained via first law ingredients, can be associated not exclusively to heat and acquire a more general meaning.
01 Jan 2006
TL;DR: In this paper, the exact expression for the convolution of gamma distributions with different scale parameters is quite complicated, and the approximation by means of another gamma distribution is shown to be remarkably accurate for wide ranges of the parameter values, in particular if more than two variables are involved.
Abstract: The exact expression for the convolution of gamma distributions with different scale parameters is quite complicated.The approximation by means of another gamma distribution is shown to be remarkably accurate for wide ranges of the parameter values, in particular if more than two variables are involved.