Modeling the amplitude statistics of ultrasonic images

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.     

Probability density of the phase of a random RF pulse in the presence of Gaussian noise

In this paper, we show that the probability density function (pdf) of the phase of a random nonstationary radio frequency (RF) impulse signal perturbed by Gaussian noise does not depend on the multiple time derivatives of the signal amplitude and phase at a given time instance and is the Bennett's pdf. Employing this revealing, we derive an alternative form of the conditional pdf of the phase representing it with the von Mises/Tikhonov pdf conditional on the envelope, signal-to-noise ratio (SNR), and signal phase. We expend this new form to the Fourier series and investigate for the locked and unlocked reference phases. The error probability for the phase to exceed a threshold is also analyzed.     

Outage mutual information of space-time MIMO channels

We derive analytical expressions for the probability density function (pdf) of the random mutual information between transmitted and received vector signals of a random space-time independent and identically distributed (i.i.d.) multiple-input multiple-output (MIMO) channel, assuming that the transmitted signals from the multiple antennas are Gaussian i.i.d.. We show that this pdf can be well approximated by a Gaussian distribution, and such a Gaussian approximation is based on expressions for the given pdfs mean and variance that we derive. We prove that at high signal-to-noise ratio (SNR), every factor of 2 increase in SNR leads to an increase in outage rate in the amount of min(M,N) bits, where M and N denote the number of transmit and receive antennas, respectively. A simple expression for the moment generating function (MGF) of the mutual information pdf is also provided, based on which we establish normality of the pdf, when both M and N are large, and the SNR is large.     

Collaborative beamforming for wireless sensor networks with Gaussian distributed sensor nodes

Collaborative beamforming has been recently introduced in the context of wireless sensor networks (WSNs) to increase the transmission range of individual sensor nodes. The challenge in using collaborative beamforming in WSNs is the uncertainty regarding the sensor node locations. However, the actual sensor node spatial distribution can be modeled by a properly selected probability density function (pdf). In this paper, we model the spatial distribution of sensor nodes in a cluster of WSN using Gaussian pdf. Gaussian pdf is more suitable in many WSN applications than, for example, uniform pdf which is commonly used for flat ad hoc networks. The average beampattern and its characteristics, the distribution of the beampattern level in the sidelobe region, and the distribution of the maximum sidelobe peak are derived using the theory of random arrays. We show that both the uniform and Gaussian sensor node deployments behave qualitatively in a similar way with respect to the beamwidths and sidelobe levels, while the Gaussian deployment gives wider mainlobe and has lower chance of large sidelobes.     

An extended Suzuki model for land mobile satellite channels and itsstatistical properties

This paper deals with the statistical characterization of a stochastic process which is a product of a Rice and lognormal process. Thereby, we consider the more general case where the two Gaussian noise processes describing the Rice process are correlated. The resulting process are named as extended Suzuki process, which can be used as a suitable statistical model for describing the fading behavior of large classes of frequency nonselective land mobile satellite channels. In particular, the statistical properties (e.g., probability density function (pdf) of amplitude and phase, level-crossing rate, and average duration of fades) of the Rice process with cross-correlated components as well as of the proposed extended Suzuki process are investigated. Moreover, all statistical model parameters are optimized numerically to fit the cumulative distribution function and the level-crossing rate of the underlying analytical model to measured data collected in different environments. Finally, an efficient simulation model is presented which is in excellent conformity with the proposed analytical model     

Unified Laguerre Polynomial-Series-Based Distribution of Small-Scale Fading Envelopes

We derive new unified probability density function (pdf) formulas based on the generalized Laguerre polynomial series expansion that cover a wide range of small-scale fading distributions in wireless communications. The unified envelope pdf covers many known Laguerre polynomial-series-based pdf's and small-scale fading distributions, which include the multiple-waves-plus-diffuse-power (MWDP) fading, kappa-mu, Nakagami-m, Rician (Nakagami-n), Nakagami-q (Hoyt), Rayleigh, Weibull, and alpha-mu (Stacy) distributions as special cases. We highlight that the unified pdf formulas are general and applicable to characterize the distribution of any random variable defined on the positive range. We then propose two truncated forms of the pdf and prove that the original pdf and both truncated forms satisfy the properties of a valid pdf. A new cumulative distribution function and a moment-generating function of this pdf are derived. We also analyze the truncation error for the case when only a finite number of terms are kept in the series expansion.     

On the Capacity of Mid-latitude High Frequency Ionospheric Channel

In this paper we consider the theoretical characterization of the ionospheric transmission. More accurately, we derive a closed form expression of the average capacity for Mid-latitude High Frequency (HF) ionospheric channels. Heretofore, this problem has been studied for Rayleigh channels when each tap of the impulse response has a Rayleigh distribution without characterizing the variance of this distribution. In this paper, we extend these works to HF ionospheric channels by evaluating the variance of the amplitude attenuation versus the Doppler spread and then the channel capacity. For a multipath HF ionospheric channel, we model the Doppler phenomenon as a Gaussian profile which is suggested for HF environments. Finally, we derive a closed form expression of the average channel capacity using the probability density function (pdf) of the instantaneous impulse response. Numerical results on both simulated and real measured data are derived at the end of the paper.     

Novel procedure to determine statistical functions of impulsive noise

One of the problems found when measuring impulsive noise is to distinguish this kind of noise from Gaussian noise. Usually, a threshold level is used to make the difference. The problem is that a high threshold level will miss low amplitude pulses, while a low level will include Gaussian noise samples as being impulsive noise. In this paper, results of a novel radio UHF impulsive noise measurement procedure are presented. This work exhibits the peculiarity that data was taken in both horizontal and vertical polarizations simultaneously. One polarization is used to determine the presence of impulsive noise so analysis can be performed in the other polarization considering this circumstance. Measurements were made in four different locations on UHF TV channels around 800 MHz with a bandwidth of 10 MHz, demodulating the in-phase and quadrature phase components in each polarization. When environments are constituted by varied and scattered impulsive sources, horizontal and vertical polarizations show similar statistical behavior. However, horizontal and vertical emissions may be different when a single source is individually measured. The conditional amplitude probability density function (pdf) and conditional amplitude cumulative distribution function (cdf) found for the amplitude in all the locations lead to the conclusion that the variable that best fits the results is a lognormal one.     

Regression on the basis of nonstationary Gaussian processes with Bayesian regularization

We consider the regression problem, i.e. prediction of a real valued function. A Gaussian process prior is imposed on the function, and is combined with the training data to obtain predictions for new points. We introduce a Bayesian regularization on parameters of a covariance function of the process, which increases quality of approximation and robustness of the estimation. Also an approach to modeling nonstationary covariance function of a Gaussian process on basis of linear expansion in parametric functional dictionary is proposed. Introducing such a covariance function allows to model functions, which have non-homogeneous behaviour. Combining above features with careful optimization of covariance function parameters results in unified approach, which can be easily implemented and applied. The resulting algorithm is an out of the box solution to regression problems, with no need to tune parameters manually. The effectiveness of the method is demonstrated on various datasets.     

Wavelet-Based SAR Image Despeckling and Information Extraction, Using Particle Filter

This paper proposes a new-wavelet-based synthetic aperture radar (SAR) image despeckling algorithm using the sequential Monte Carlo method. A model-based Bayesian approach is proposed. This paper presents two methods for SAR image despeckling. The first method, called WGGPF, models a prior with Generalized Gaussian (GG) probability density function (pdf) and the second method, called WGMPF, models prior with a Generalized Gaussian Markov random field (GGMRF). The likelihood pdf is modeled using a Gaussian pdf. The GGMRF model is used because it enables texture parameter estimation. The prior is modeled using GG pdf, when texture parameters are not needed. A particle filter is used for drawing particles from the prior for different shape parameters of GG pdf. When the GGMRF prior is used, the particles are drawn from prior in order to estimate noise-free wavelet coefficients and for those coefficients the texture parameter is changed in order to obtain the best textural parameters. The texture parameters are changed for a predefined set of shape parameters of GGMRF. The particles with the highest weights represents the final noise-free estimate with corresponding textural parameters. The despeckling algorithms are compared with the state-of-the-art methods using synthetic and real SAR data. The experimental results show that the proposed despeckling algorithms efficiently remove noise and proposed methods are comparable with the state-of-the-art methods regarding objective measurements. The proposed WGMPF preserves textures of the real, high-resolution SAR images well.     

Neural Network Inverse Modeling and Applications to Microwave Filter Design

In this paper, systematic neural network modeling techniques are presented for microwave modeling and design using the concept of inverse modeling where the inputs to the inverse model are electrical parameters and outputs are geometrical parameters. Training the neural network inverse model directly may become difficult due to the nonuniqueness of the input-output relationship in the inverse model. We propose a new method to solve such a problem by detecting multivalued solutions in training data. The data containing multivalued solutions are divided into groups according to derivative information using a neural network forward model such that individual groups do not have the problem of multivalued solutions. Multiple inverse models are built based on divided data groups, and are then combined to form a complete model. A comprehensive modeling methodology is proposed, which includes direct inverse modeling, segmentation, derivative division, and model combining techniques. The methodology is applied to waveguide filter modeling and more accurate results are achieved compared to the direct neural network inverse modeling method. Full electromagnetic simulation and measurement results of Ku-band circular waveguide dual-mode pseudoelliptic bandpass filters are presented to demonstrate the efficiency of the proposed neural network inverse modeling methodology.     

New cumulative damage models for failure using stochastic processes as initial damage

Based on a generalized cumulative damage approach with a stochastic process describing initial damage for a material specimen, a broad class of statistical models for material strength is developed. Plausible choices of stochastic processes for the initial damage include Brownian motion, geometric Brownian motion, and the gamma process; and additive & multiplicative cumulative damage functions are considered. The resulting general statistical model gives an accelerated test form of the inverse Gaussian distribution, special cases of which include some existing models in addition to several new models. Model parameterizations & estimation by maximum likelihood from accelerated test data are discussed, and the applicability of the general model is illustrated for three sets of strength data. The proposed models are compared with the power-law Weibull model, and the inverse Gaussian generalized linear models.     

Designing Time-Hopping Ultrawide Bandwidth Receivers for Multiuser Interference Environments

The multiple-user interference (MUI) in time-hopped impulse-radio ultrawide bandwidth (UWB) systems is impulse-like and poorly approximated by a Gaussian distribution. Therefore, conventional matched filter receiver designs, which are optimal for Gaussian noise, are not fully efficient for UWB applications. Several alternative distributions for approximating the MUI process and the MUI-plus-noise process in UWB systems are motivated and compared. These distributions have in common that they are more impulsive than the Gaussian approximation, with a greater area in the tails of the probability density function (pdf) compared to a Gaussian pdf. The improved MUI and MUI-plus-noise models are utilized to derive new receiver designs for UWB applications, which are shown to be superior to the conventional matched filter receiver. Multipath propagation is abundant in UWB channels and is exploited by a Rake receiver. A Rake receiver uses multiple fingers to comb the multipath rays with a conventional matched filter implemented in each finger. Rake structures utilizing the new receiver designs that are suitable for reception of UWB signals in multipath fading channels are provided. An optimal performance benchmark, based on an accurate theoretical model for the interference that fully explains the features of the MUI pdf, is also presented. Analysis and simulation results are shown for the novel receivers, which demonstrate that the new designs have superior performance compared to the conventional linear receiver when MUI is significant. Several adaptive receivers are shown to always match or exceed the performance of the conventional linear receiver in all MUI-plus-noise environments. Parameter estimation for the new receivers also is discussed.      

The first passage time distribution of brownian motion and its applications

This paper traces the development of the first passage time distribution of Brownian motion (inverse Gaussian) together with its various applications in inventory problems, usage and storage times, detection theory, labor turnover, money supply, purchasing models, hospital inpatient stay times, strikes duration, biology, … etc. Besides, since the inverse Gaussian distribution arises as the distribution of first passage time of Brownian motion, its applicability to lifetime modeling is a natural consequence. The general characteristics of the inverse Gaussian model which make it attractive for various applications are also identified.     

A Nakagami-N-gamma Model for Shadowed Fading Channels

Wireless channels are subject to short term fading and shadowing. Such shadowed fading channels are described using a Nakagami-lognormal process, with the Nakagami-m (short term fading) and lognormal distributions (shadowing). This approach does not result in a closed form solution for the density function of the signal-to-noise ratio (SNR) making wireless systems analysis difficult. It was suggested that a gamma or an inverse Gaussian distribution can be used in place of the lognormal distribution providing an analytical framework. The match of these two distributions to the lognormal was less than ideal. Invoking shadowing as multiplicative process, the distribution of the product of N gamma variables is proposed in place of the lognormal pdf resulting in the Nakagami-N-gamma model. It is shown that this model leads to simple solutions to the density and distribution functions as well as error rates for coherent phase shift keying modems. The outage probabilities and error rates based on the Nakagami-lognormal (NL) and Nakagami-N-gamma (NNG) models were compared. Results showed excellent match at levels of shadowing generally observed in wireless systems. While values of N as low as 3 was sufficient for low values of m and weak to moderate shadowing, values of N in the range of 7–9 provided better match for higher levels of shadowing and higher values of m. By varying N, it is also possible to get the NNG pdf to move closer to the NL pdf making the new model an ideal one for the shadowed fading channels with its flexibility and availability of analytical expressions.     

混合因子分析的重新抽样方法

混合因子分析是一种对具有复杂结构的多维数据建立模型的方法.本文提出了一种进行混合因子分析的重新抽样方法.当给定一组数据样本时,我们首先建立样本概率分布的混合高斯模型,然后为每一个高斯混合项重新抽取新的数据样本,在新的样本上再对每一个高斯混合项进行因子分析.与已有的算法相比较,避免了计算各个高斯混合项在每个样本值之下的后验概率,又减少了进行因子分析时参与计算的数据样本的数量.     

Statistical behavior of edge detectors

In this paper we present a method for estimating the statistical properties of two well-known edge detectors: the non maxima suppression and the zero crossing of the Laplacian algorithms. Assuming the data are corrupted by an additive Gaussian noise we derive the probability density function (pdf) of the detected edge. Thanks to this approach the computed pdf explicitly depends on the parameters of the edge detector. Experimental results on real images and comparisons with Monte Carlo simulations are presented in order to characterize the performance of this method.     

Novel distribution model of transformed coefficients in video coding using quad-tree structured block partitioning

Today’s video coding standard such as high efficiency video coding uses a full quad-tree structured block partitioning, so the underlying statistics of transformed coefficients becomes more complicated to estimate than the previous standards due to the coding structure. However, a statistical distribution of transformed residue is important for a design of a smart encoder. Thus, in this paper, we present a theoretic analysis of a distribution of transformed coefficients produced from an encoder using different transform sizes, and derive a probability density function (pdf) for the estimation. The proposed density model provides a more accurate distribution model than the conventional pdfs. Parameters are theoretically estimated, and rate-distortion model is established from the proposed pdf. We also apply the proposed method to a rate control problem to show the efficiency of the proposed density model. Our experimental results show that the proposed method is better capable of modeling the mixed sources of multiple-type transform coefficients occurred from the quad-tree coding structure of transform and provides an accurate estimate in rate control.

     

A study of relative phase in complex wavelet domain: Property,statistics and applications in texture image retrieval and segmentation

In this paper, we develop a new approach which exploits the probabilistic properties from the phase information of 2-D complex wavelet coefficients for image modeling. Instead of directly using phases of complex wavelet coefficients, we demonstrate why relative phases should be used. The definition, properties and statistics of relative phases of complex coefficients are studied in detail. We proposed von Mises and wrapped Cauchy for the probability density function (pdf) of relative phases in the complex wavelet domain. The maximum-likelihood method is used to estimate two parameters of von Mises and wrapped Cauchy. We demonstrate that the von Mises and wrapped Cauchy fit well with real data obtained from various real images including texture images as well as standard images. The von Mises and wrapped Cauchy models are compared, and the simulation results show that the wrapped Cauchy fits well with the peaky and heavy-tailed pdf of relative phases and the von Mises fits well with the pdf which is in Gaussian shape. For most of the test images, the wrapped Cauchy model is more accurate than the von Mises model, when images are decomposed by different complex wavelet transforms including dual-tree complex wavelet (DTCWT), pyramidal dual-tree directional filter bank (PDTDFB) and uniform discrete curvelet transform (UDCT). Moreover, the relative phase is applied to obtain new features for texture image retrieval and segmentation applications. Instead of using only real or magnitude coefficients, the new approach uses a feature in which phase information is incorporated, yielding a higher accuracy in texture image retrieval as well as in segmentation. The relative phase information which is complementary to the magnitude is a promising approach in image processing.     

Optimization of LDPC-coded turbo CDMA systems

We consider the analysis and design of low-density parity-check (LDPC) codes for turbo multiuser detection in multipath code division multiple access (CDMA) channels. We develop techniques for computing the probability density function (pdf) of the extrinsic messages at the output of the soft-input soft-output (SISO) multiuser detectors as a function of the pdf of input extrinsic messages, user spreading codes, channel impulse responses, and signal-to-noise ratios. Of particular interest is the soft interference cancellation plus minimum mean square error (SIC-MMSE) multiuser detector, for which the pdf of the extrinsic messages can be characterized analytically. For the case of additive white Gaussian noise (AWGN) channels, the extrinsic messages can be well approximated as symmetric Gaussian distributed. For the case of asynchronous multipath fading channels, the extrinsic messages can be approximated by a mixture of symmetric Gaussian distributions. We show that the expectation-maximization (EM) algorithm can be used to compute the parameters of this mixture. Using these techniques, we are able to accurately compute the thresholds for LDPC codes and design good irregular LDPC codes. Simulation results are in good agreement with the computed thresholds, and the designed irregular LDPC codes outperform regular ones significantly.