Probability density function for the phase and frequency noise in a semiconductor laser

A physical definition for the phase and frequency noise of a semiconductor laser is given, which can be applied in determining the performance of coherent optical communication systems. The definition allows a filtered Poisson model to be developed for the probability density function (pdf) of the laser output phase or frequency noise, based on evaluating the cumulants of the noise processes. A condition is derived to quantify under what laser and system conditions a Gaussian pdf is a good approximation. It is shown that the phase and frequency noise can increase significantly for bit rates approaching the relaxation oscillation frequency of the laser diode.     

激光尘埃粒子计数器信号幅度概率密度函数

为了研究激光尘埃粒子计数器计数信号幅度概率分布,对激光尘埃粒子计数器计数信号幅度概率分布与传感器光敏区光强分布、采样气流中的粒子数密度、气体层流速度分布之间的关系进行了理论分析。采用自行设计的带保护气套的光电传感器测定粒子计数信号幅度概率分布,给出的分布模型与理论分析相吻合。结果表明,尘埃粒子计数器计数信号幅度概率分布由传感器光敏区光强分布和粒子数密度空间分布共同决定,这为尘埃粒子计数器的设计提供了理论依据。     

Dictionary-based stochastic expectation-maximization for SAR amplitude probability density function estimation

In remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of the pixel intensities. This paper deals with the problem of probability density function (pdf) estimation in the context of synthetic aperture radar (SAR) amplitude data analysis. Several theoretical and heuristic models for the pdfs of SAR data have been proposed in the literature, which have been proved to be effective for different land-cover typologies, thus making the choice of a single optimal parametric pdf a hard task, especially when dealing with heterogeneous SAR data. In this paper, an innovative estimation algorithm is described, which faces such a problem by adopting a finite mixture model for the amplitude pdf, with mixture components belonging to a given dictionary of SAR-specific pdfs. The proposed method automatically integrates the procedures of selection of the optimal model for each component, of parameter estimation, and of optimization of the number of components by combining the stochastic expectation-maximization iterative methodology with the recently developed "method-of-log-cumulants" for parametric pdf estimation in the case of nonnegative random variables. Experimental results on several real SAR images are reported, showing that the proposed method accurately models the statistics of SAR amplitude data.     

On the estimation of bispectral density function in the case ofrandomly missing observations

The estimation of the bispectral density function of a stationary stochastic process when some observations are missing according to a point binomial distribution is considered in the paper. The existence of the bispectrum, and its estimation are considered. The methods are illustrated with simulated examples     

On the probability density estimation

A modification of algorithms obtained previously for estimating the probability density function is presented. The proposed approach permits the derivation of an analytical approximation for which the normalization condition is always satisfied.     

Fast medical image mixture density clustering segmentation using stratification sampling and kernel density estimation

The Gaussian mixture models (GMMs) is a flexible and powerful density clustering tool. However, the application of it to medical image segmentation faces some difficulties. First, estimation of the number of components is still an open question. Second, the speed of it for large medical image is slow. Moreover, GMMs has the problem of noise sensitivity. In this paper, the kernel density estimation method is used to estimate the number of components K, and three strategies are proposed to improve the segmentation speed of GMMs. First, a histogram stratification sampling strategy is proposed to reduce the size of the training data. Second, a binning strategy is proposed to search the neighbor points of each center data to compute the approximate density function of the samples. Third, a hill-climbing algorithm with the dynamic step size is designed to find the local maxima of the density function. The kernel density estimation method and sampling technology reduce the effect of noise. Experimental results with the simulated brain images and real CT images show that the proposed algorithm has better performance in generating explainable segmentations with faster speed than the common GMMs algorithm.     

利用核密度估计的空基视频运动目标检测

介绍了一种基于核密度估计的空基视频运动目标检测方法.首先,采用特征点对应法进行全局运动估计,根据特征点间的相互位置关系,剔除无效的特征点对,提高全局运动估计精度.并通过背景运动补偿,获取背景相对静止的图像序列;采用非参数核密度估计法进行背景建模,通过背景差分法实现运动目标检测,同时分析了检测噪声产生的主要因素,并采用检...     

利用背景高斯核密度估计的运动目标检测方法

运动目标检测是当前计算机视觉、图像理解、信号处理领域的研究热点之一,在研究了现有大量算法的基础上,通过比较各种算法之间的有效性,并结合工程实际,提出了一种利用图像灰度信息进行背景高斯核密度估计的运动目标检测方法.由于该方法保留了背景的多个模态,通过引入面积阈值来消除大的噪声和判断背景是否发生了突变,当出现大的噪声未被消除或者背景发生突变的情况时,能够重新更新背景样本集,适应背景突变.实验结果表明:该方法不仅可以很好地处理背景中存在周期运动干扰的情况,并且可以适应背景突变,较好地去除了虚警、误警,有效地降低了摄像机抖动、树叶摇动、下雨天气等背景复杂情况下的误检率,准确地检测到了运动目标.     

Estimation of probability density function using spectral analysis

The authors present a new bound on the estimation of the probability density function of random signals, using Woodward's theorem, correlation techniques and spectral analysis. The proposed method is based on the spectral analysis of the random process     

Probability density functions of soft information

It is well known that soft decoding algorithms are based on the use of reliability measures for binary and nonbinary symbols. We consider an analytical estimation of the distributions of reliability measures after soft decoding of block and convolutional codes or intersymbol interference (ISI) channels. This estimation, based on a simple geometric interpretation of reliability measures, allows the observation of different distributions for correct and incorrect symbols, and could be helpful for the analysis of soft decoding algorithms     

Bayesian and non-Bayesian estimation for the pareto parameters using quasi-likelihood function

The quasi-likelihood function is used to derive Bayesian and non-Bayesian estimates for the unknown parameters of the Pareto distribution. In the Bayesian technique the likelihood function is replaced with the quasi-likelihood function when the mean-variance relationship is defined. The efficiency of the quasi-likelihood estimation relative to the maximum likelihood is calculated. Numerical illustrations for the Bayesian and quasi-Bayesian procedures are given.     

A Bayesian estimation of reliability model using the linex loss function

In this paper the problem of Bayes estimation of the reliability and the shape parameter p of a finite range failure time model is considered (assuming scale parameter θ is known). Following Zellner [A. Zellner, J. Am. Statist. Assoc. 81, 446–451 (1986)] the asymmetric loss function is used to obtain the Bayes estimators. Efficiencies of the proposed Bayes estimators are obtained with respect to the ordinary Bayes estimators and it was found that the proposed Bayes estimators are better than the ordinary Bayes estimators for quite a wide range of parameters.     

Detection and estimation using an adaptive rational function filter

Proposes a new nonlinear adaptive filter structure based on rational functions. There are several advantages to the use of this filter. First, it is a universal approximator and a good extrapolator. Second, it ran be trained by a linear adaptive algorithm, which makes it suitable for real-time adaptive signal processing. Third, it has a best approximation for a specified function. To demonstrate its utility as a tool for solving adaptive signal processing problems, the authors apply the adaptive rational function filter to the problem of estimation and detection. The estimation problem pertains to the direction of arrival (DOA) estimation problem in array signal processing. For the detection problem, the authors consider the detection of a weak radar target (a small piece of ice) in an ocean environment     

Probability estimation in arithmetic and adaptive-Huffman entropycoders

Entropy coders, such as Huffman and arithmetic coders, achieve compression by exploiting nonuniformity in the probabilities under which a random variable to be coded takes on its possible values. Practical realizations generally require running adaptive estimates of these probabilities. An analysis of the relationship between estimation quality and the resulting coding efficiency suggests a particular scheme, dubbed scaled-count, for obtaining such estimates. It can optimally balance estimation accuracy against a need for rapid response to changing underlying statistics. When the symbols being coded are from a binary alphabet, simple hardware and software implementations requiring almost no computation are possible. A scaled-count adaptive probability estimator of the type described in this paper is used in the arithmetic coder of the JBIG and JPEG image coding standards.     

Sequential nonparametric density estimation

Using kernel estimates of the Parzen type, a naive sequential nonparametric density estimation procedure is developed. The asymptotic distribution structure of the stopping variable is examined. The stopping variable is shown to have finite moments of ail order and is shown to be dosed. The stopping variableNdepends on some preassigned errorvarepsilon, and it is shown thatNdiverges strongly toinftyasvarepsilonconverges to zero. Finally, withhat{f}_n(x)being a kernel-type estimator, it is shown thathat{f}_N(X)converges tof(x), the true density atx, with probability one asvarepsilonconverges to zero.     

The estimation of the gradient of a density function, with applications in pattern recognition

Nonparametric density gradient estimation using a generalized kernel approach is investigated. Conditions on the kernel functions are derived to guarantee asymptotic unbiasedness, consistency, and uniform consistency of the estimates. The results are generalized to obtain a simple mcan-shift estimate that can be extended in ak-nearest-neighbor approach. Applications of gradient estimation to pattern recognition are presented using clustering and intrinsic dimensionality problems, with the ultimate goal of providing further understanding of these problems in terms of density gradients.     

SAR amplitude probability density function estimation based on a generalized Gaussian model.

In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed "method-of-log-cumulants" (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena.     

Probability density functions of amplitude-modulated random signals

The probability density function arising from multiplication of two independent random variables has been extensively treated by statisticians, yet some common signal processing product situations have not been analysed. An important example of this omission is the amplitude modulation of a Gaussian process. Here, a little-known Hankel transform-based procedure provides a ready solution for this problem and many other types of random modulation signals. Several new modulation results are tabulated in graphical form and it is also shown that half-amplitude sinusoidal processes added yield the same distribution as their (unit-amplitude) product