HMM-WC-FNM模型在触头表面形貌去噪中的应用

本文提出了一种可靠的图像去噪算法,基于观察图像是期望图像叠加了不规则噪声的假设,用有限高斯混合分布(FNM)描述期望图像分解小波系数(WC)的先验分布,用隐马尔可夫模型(HMM)描述同一方向不同分解级之间的小波系数的依赖关系,采用Bayes准则,根据期望图像的后验分布(以观测图像为条件)所对应的HMM模型的条件概率,用EM(expectation maximization)优化算法,获得MAP(maximization a posteriori)准则下的去噪图像。针对银基触头材料表面形貌去噪对几种算法作定性比较,并对去噪性能给出定量分析,仿真结果表明,此方法有效去除噪声的同时,能保留原始图像的细节信息。     

Wavelet-Based Semiblind Channel Estimation for Ultrawideband OFDM Systems

Ultrawideband (UWB) communications involve very sparse channels, because the bandwidth increase results in a better time resolution. This property is used in this paper to propose an efficient algorithm that jointly estimates the channel and the transmitted symbols. More precisely, this paper introduces an expectation-maximization (EM) algorithm within a wavelet-domain Bayesian framework for semiblind channel estimation of multiband orthogonal frequency division multiplexing based UWB communications. A prior distribution is chosen for the wavelet coefficients of the unknown channel impulse response to model a sparseness property of the wavelet representation. This prior yields, in maximum a posteriori estimation, a thresholding rule within the EM algorithm. We particularly focus on reducing the number of estimated parameters by iteratively discarding “insignificant” wavelet coefficients from the estimation process. Simulation results using UWB channels that were issued from both models and measurements show that, under sparseness conditions, the proposed algorithm outperforms pilot-based channel estimation in terms of the mean square error (MSE) and bit error rate (BER). Moreover, the estimation accuracy is improved, whereas the computational complexity is reduced compared with traditional semiblind methods.      

Bayesian pixel classification using spatially variant finitemixtures and the generalized EM algorithm

A spatially variant finite mixture model is proposed for pixel labeling and image segmentation. For the case of spatially varying mixtures of Gaussian density functions with unknown means and variances, an expectation-maximization (EM) algorithm is derived for maximum likelihood estimation of the pixel labels and the parameters of the mixture densities, An a priori density function is formulated for the spatially variant mixture weights. A generalized EM algorithm for maximum a posteriori estimation of the pixel labels based upon these prior densities is derived. This algorithm incorporates a variation of gradient projection in the maximization step and the resulting algorithm takes the form of grouped coordinate ascent. Gaussian densities have been used for simplicity, but the algorithm can easily be modified to incorporate other appropriate models for the mixture model component densities. The accuracy of the algorithm is quantitatively evaluated through Monte Carlo simulation, and its performance is qualitatively assessed via experimental images from computerized tomography (CT) and magnetic resonance imaging (MRI).     

Maximum-likelihood versus maximum a posteriori parameter estimation of physiological system models: the C-peptide impulse response case study

Maximum-likelihood (ML), also given its connection to least-squares (LS), is widely adopted in parameter estimation of physiological system models, i.e., assigning numerical values to the unknown model parameters from the experimental data. A more sophisticated but less used approach is maximum a posteriori (MAP) estimation. Conceptually, while ML adopts a Fisherian approach, i.e., only experimental measurements are supplied to the estimator, MAP estimation is a Bayesian approach, i.e., a priori available statistical information on the unknown parameters is also exploited for their estimation. In this paper, after a brief review of the theory behind ML and MAP estimators, we compare their performance in the solution of a case study concerning the determination of the parameters of a sum of exponential model which describes the impulse response of C-peptide (CP), a key substance for reconstructing insulin secretion. The results show that MAP estimation always leads to parameter estimates with a precision (sometimes significantly) higher than that obtained through ML, at the cost of only a slightly worse fit. Thus, a three exponential model can be adopted to describe the CP impulse response model in place of the two exponential model usually identified in the literature by the ML/LS approach. Simulated case studies are also reported to evidence the importance of taking into account a priori information in a data poor situation, e.g., when a few or too noisy measurements are available. In conclusion, our results show that, when a priori information on the unknown model parameters is available, Bayes estimation can be of relevant interest, since it can significantly improve the precision of parameter estimates with respect to Fisher estimation. This may also allow the adoption of more complex models than those determinable by a Fisherian approach.     

Estimation of Constrained Parameters With Guaranteed MSE Improvement

We address the problem of estimating an unknown parameter vector x in a linear model y=Cx+v subject to the a priori information that the true parameter vector x belongs to a known convex polytope X. The proposed estimator has the parametrized structure of the maximum a posteriori probability (MAP) estimator with prior Gaussian distribution, whose mean and covariance parameters are suitably designed via a linear matrix inequality approach so as to guarantee, for any xisinX, an improvement of the mean-squared error (MSE) matrix over the least-squares (LS) estimator. It is shown that this approach outperforms existing "superefficient" estimators for constrained parameters based on different parametrized structures and/or shapes of the parameter membership region X     

Fast adaptive equalization/diversity combining for time-varyingdispersive channels

We examine adaptive equalization and diversity combining methods for fast Rayleigh-fading frequency selective channels. We assume a block adaptive receiver in which the receiver coefficients are obtained from feedforward channel estimation. For the feedforward channel estimation, we propose a novel reduced dimension channel estimation procedure, where the number of unknown parameters are reduced using a priori information of the transmit shaping filter's impulse response. Fewer unknown parameters require a shorter training sequence. We obtain least-squares, maximum-likelihood, and maximum a posteriori (MAP) estimators for the reduced dimension channel estimation problem. For symbol detection, we propose the use of a matched filtered diversity combining decision feedback equalizer (DFE) instead of a straightforward diversity combining DFE. The matched filter form has lower computational complexity and provides a well-conditioned matrix inversion. To cope with fast time-varying channels, we introduce a new DFE coefficient computation algorithm which is obtained by incorporating the channel variation during the decision delay into the minimum mean square error (MMSE) criterion. We refer to this as the non-Toeplitz DFE (NT-DFE). We also show the feasibility of a suboptimal receiver which has a lower complexity than a recursive least squares adaptation, with performance close to the optimal NT-DFE     

Nonparametric multivariate density estimation: a comparative study

The paper algorithmically and empirically studies two major types of nonparametric multivariate density estimation techniques, where no assumption is made about the data being drawn from any of known parametric families of distribution. The first type is the popular kernel method (and several of its variants) which uses locally tuned radial basis (e.g., Gaussian) functions to interpolate the multidimensional density; the second type is based on an exploratory projection pursuit technique which interprets the multidimensional density through the construction of several 1D densities along highly “interesting” projections of multidimensional data. Performance evaluations using training data from mixture Gaussian and mixture Cauchy densities are presented. The results show that the curse of dimensionality and the sensitivity of control parameters have a much more adverse impact on the kernel density estimators than on the projection pursuit density estimators     

Partial update and sparse adaptive filters

There has been increasing research interest in developing adaptive filters with partial update (PU) and adaptive filters for sparse impulse responses. On the basis of maximum a posteriori (MAP) estimation, new adaptive filters are developed by determining the update when a new set of training data is received. The MAP estimation formulation permits the study of a number of different prior distributions which naturally incorporate the sparse property of the filter coefficients. First, the Gaussian prior is studied, and a new adaptive filter with PU is proposed. A theoretical basis for an existing PU adaptive filter is also studied. Then new adaptive filters that directly exploit the sparsity of the filter are developed by using the scale mixture Gaussian distribution as the prior. Two new algorithms based on the Student's-t and power-exponential distributions are presented. The minorisation-maximisation algorithm is employed as an optimisation tool. Simulation results show that the learning performance of the proposed algorithms is better than or similar to that of some recently published algorithms     

A per-survivor phase-estimation algorithm for detection of PSKsignals

An expectation-maximization (EM) technique for maximum a posteriori (MAP) estimation of a random parameter is employed to devise a per-survivor phase-tracking algorithm for phase-shift-keyed signals transmitted over channels with phase jitter. Simulation results show that the proposed algorithm can provide substantial performance gains over recursive and nonrecursive phase estimators in the presence of a strong phase jitter     

A radar application of a modified Cramer-Rao bound: parameterestimation in non-Gaussian clutter

In this paper, we derive a lower bound on the error covariance matrix for any unbiased estimator of the parameters of a signal composed of a mixture of spherically invariant random processes (SIRPs). The proposed approach represents a special case of the global Cramer-Rao bound for hybrid random and deterministic parameters estimation, and it is particularly useful when the data, conditioned on a vector of unwanted random parameters (nuisance parameters) with a priori known probability density function, can be modeled as a Gaussian vector. The case of signal composed of a mixture of K-distributed clutter, Gaussian clutter, and thermal noise belongs to this set, and it is regarded as a realistic radar scenario. In the radar problem considered here, this bound can be numerically computed in closed-form, whereas the computation of the true (marginal) Cramer-Rao bound turns out to be infeasible. The performance of some practical estimators are compared with it for two study cases     

有限贝塔刘维尔混合模型的变分学习及其应用

由于贝塔刘维尔分布的共轭先验分布中存在积分表达式,贝叶斯估计有限贝塔刘维尔混合模型参数异常困难.本文提出利用变分贝叶斯学习模型参数,采用gamma分布作为近似的先验分布并使用合理的非线性近似技术,得到了后验分布的近似解.与常用的EM算法相比,该方法能够同时估计模型参数和确定分量数,且避免了过拟合的问题.在合成数据集及场景分类问题上进行了大量的实验,实验结果验证了本文所提方法的有效性.     

MIMO-OFDM系统中一种改进的Bayesian EM信道估计器

该文提出了MIMO-OFDM系统中一种改进的Bayesian EM信道估计器。利用软球形译码器的搜索列表和解码器反馈的先验信息对传统EM信道估计中的软信息近似处理进行了修正,计算了更为准确的软符号后验概率分布以及一阶、二阶统计量。基于初始估计得到的信道先验信息,设计了新的考虑软符号后验互相关的时域信道冲激响应最大后验概率(MAP)估计算法。仿真试验结果表明:该算法和传统EM信道估计算法相比具有更低的误码率和更小的估计均方误差值。     

Markovian Arrival Process Parameter Estimation With Group Data

This paper addresses a parameter estimation problem of Markovian arrival process (MAP). In network traffic measurement experiments, one often encounters the group data where arrival times for a group are collected as one bin. Although the group data are observed in many situations, nearly all existing estimation methods for MAP are based on nongroup data. This paper proposes a numerical procedure for fitting a MAP and a Markov-modulated Poisson process (MMPP) to group data. The proposed algorithm is based on the expectation-maximization (EM) approach and is a natural but significant extension of the existing EM algorithms to estimate parameters of the MAP and MMPP. Specifically for the MMPP estimation, we provide an efficient approximation based on the proposed EM algorithm. We examine the performance of proposed algorithms via numerical experiments and present an example of traffic analysis with real traffic data.      

Efficient parameter estimation of partially polarizedelectromagnetic waves

The paper considers the problem of statistically efficient estimation of the parameters of partially polarized electromagnetic (EM) waves with a uniform linear array of crossed dipoles. Previous research considered only completely polarized EM waves. The authors consider the maximum likelihood (ML) estimation of partially polarized wave parameters, in particular, the incident angles and the degrees of polarization. They present a computationally efficient large-sample ML estimator that avoids the multidimensional search over the parameter space, which is required by the exact ML estimator. They also show how to deal with the cases where some of the incident waves are known or are considered to be completely polarized. Finally, some numerical examples comparing the performance of the estimators with their theoretical statistical performance in a variety of scenarios are presented     

A MAP Estimator for the m Parameter in Nakagami Fading Ultra-Wide Bandwidth Indoor Channels

A maximum a posteriori (MAP) estimator for the Nakagami m parameter in an ultra-wide bandwidth (UWB) indoor channel is proposed. Previous work exclusively studies maximum likelihood (ML) estimation and moment method (MM) estimation of the Nakagami m parameter. This letter derives the MAP estimator for the Nakagami m parameter by using the a priori probabilities of the Nakagami fading parameters in an indoor UWB channel. The performance of the MAP estimator is examined and compared with those of the ML estimator and the MM estimator. Numerical results demonstrate that the new MAP estimator is superior to the ML estimator and the MM estimator in an indoor UWB channel, especially when the sample size in the estimation is small     

Bayesian estimation and prediction for Burr‐Rayleigh mixture model using censored data

In this study, Burr‐XII and Rayleigh distributions are combined to form a new mixture model that is considered to model heterogeneous data. Our objective is to estimate parameters of the proposed mixture model using Bayesian technique under type‐I censoring. Bayesian parameter estimation for the said mixture model is conducted by using informative priors, ie, gamma and squared root inverted gamma (SRIG) as well as noninformative prior, ie, Jeffrey's prior. Squared error loss function (SELF) and quadratic loss function (QLF) are employed to obtain and Bayes estimators. Properties of the proposed Bayes estimators are highlighted through a simulation study. When prior distributions and loss functions utilized in the study are compared in terms of posterior risks, informative prior found to be more suitable and decision turns out to be in favor of QLF. Prediction limits for the single sample case and two sample case are obtained to provide an insight into future sample data. Application of the proposed model is also elaborated using a real‐life example.     

Medical image segmentation based on non-parametric mixture models with spatial information

Because of too much dependence on prior assumptions, parametric estimation methods using finite mixture models are sensitive to noise in image segmentation. In this study, we developed a new medical image segmentation method based on non-parametric mixture models with spatial information. First, we designed the non-parametric image mixture models based on the cosine orthogonal sequence and defined the spatial information functions to obtain the spatial neighborhood information. Second, we calculated the orthogonal polynomial coefficients and the mixing ratio of the models using expectation-maximization (EM) algorithm, to classify the images by Bayesian Principle. This method can effectively overcome the problem of model mismatch, restrain noise, and keep the edge property well. In comparison with other methods, our method appears to have a better performance in the segmentation of simulated brain images and computed tomography (CT) images.     

Discrete visual features modeling via leave-one-out likelihood estimation and applications

Discrete data are an important component in many image processing and computer vision applications. In this work we propose an unsupervised statistical approach to learn structures of this kind of data. The central ingredient in our model is the introduction of the generalized Dirichlet distribution as a prior to the multinomial. An estimation algorithm, based on leave-one-out likelihood and empirical Bayesian inference, for the parameters is developed. This estimation algorithm can be viewed as a hybrid expectation–maximization (EM) which alternates EM iterations with Newton–Raphson iterations using the Hessian matrix. We propose then the use of our model as a parametric basis for support vector machines within a hybrid generative/discriminative framework. In a series of experiments involving scene modeling and classification using visual words, and color texture modeling we show the efficiency of the proposed approach.     

Maximum Likelihood Unsupervised Source Separation in Gaussian Noise

This paper presents a new Maximum Likelihood (ML) based approach to the separation of convolutive mixtures of unobserved sources in the presence of Additive Gaussian Noise (AGN). The proposed method proceeds in two steps. First, the mixing system coefficients are estimated in the ML sense and, afterwards, this information is employed to attain source separation according to either the ML or the linear Minimum Mean Square Error (MMSE) criteria. System coefficient estimation is carried out in a block-iterative way using an extension of the Expectation Maximization (EM) method. Both deterministic and stochastic (Monte Carlo) implementations of the resulting estimation algorithm are considered. The proposed algorithms rely on the knowledge of the sources joint probability density function (p.d.f.). This is a fairly realistic assumption in applications such as digital communications but computer simulations reveal that it is not an stringent requirement. The proposed estimation algorithm can be successfully used with a tentative p.d.f. when this is not known a priori.