A smoothness priors long AR model method for spectral estimation

A new smoothness priors long AR model method approach is taken to the short data span spectral estimation problem. An autoregressive (AR) model that is relatively long compared to the data length is considered. The smoothness priors are in the form of the integrated squared derivatives of the AR model whitening filter. A smoothness tradeoff parameter or Bayesian hyperparameter balances the tradeoff between the infidelity of the AR model to the data and the infidelity of the model to the smoothness constraint. The critical computation of the likelihood of the hyperparameters of the Bayesian model is realized by a constrained least squares computation. Numerical examples are shown. The results of simulation studies using entropy comparison evaluations of the Bayesian and minimum AIC-AR methods of spectral estimation are also shown.     

Speech enhancement using a Bayesian evidence approach

We consider the enhancement of speech corrupted by additive white Gaussian noise. In a Bayesian inference framework, maximum a posteriori (MAP) estimation of the signal is performed, along the lines developed by Lim & Oppenheim (1978). The speech enhancement problem is treated as a signal estimation problem, whose aim is to obtain a MAP estimate of the clean speech signal, given the noisy observations. The novelty of our approach, over previously reported work, is that we relate the variance of the additive noise and the gain of the autoregressive (AR) process to hyperparameters in a hierarchical Bayesian framework. These hyperparameters are computed from the noisy speech data to maximize the denominator in Bayes formula, also known as the evidence. The resulting Bayesian scheme is capable of performing speech enhancement from the noisy data without the need for silence detection. Experimental results are presented for stationary and slowly varying additive white Gaussian noise. The Bayesian scheme is also compared to the Lim and Oppenheim system, and the spectral subtraction method.     

A blind separation method of overlapped multi-components based on time varying AR model

A method utilizing single channel recordings to blindly separate the multicomponents overlapped in time and frequency domains is proposed in this paper. Based on the time varying AR model, the instantaneous frequency and amplitude of each signal component are estimated respectively, thus the signal component separation is achieved. By using prolate spheroidal sequence as basis functions to expand the time varying parameters of the AR model, the method turns the problem of linear time varying parameters estimation to a linear time invariant parameter estimation problem, then the parameters are estimated by a recursive algorithm. The computation of this method is simple, and no prior knowledge of the signals is needed. Simulation results demonstrate validity and excellent performance of this method.     

时变迭合AR模型的参数估计*

首次提出了时变迭合ＡＲ模型,该模型在实际应用中具有广泛的应用价值．应用两步最小二乘法和限定记忆递推最小二乘法,给出了模型中时变参数的递推估计算法,该算法仅依靠量测数据即能自适应进行．仿真计算及应用结果表明：算法能够自适应地跟踪量测数据模型参数的变化,效果是令人满意的．     

Denoising of multicomponent images using wavelet least-squares estimators

In this paper, we study denoising of multicomponent images. The presented procedures are spatial wavelet-based denoising techniques, based on Bayesian least-squares optimization procedures, using prior models for the wavelet coefficients that account for the correlations between the spectral bands. We analyze three mixture priors: Gaussian scale mixture models, Bernoulli-Gaussian mixture models and Laplacian mixture models. These three prior models are studied within the same framework of least-squares optimization. The presented procedures are compared to Gaussian prior model and single-band denoising procedures. We analyze the suppression of non-correlated as well as correlated white Gaussian noise on multispectral and hyperspectral remote sensing data and Rician distributed noise on multiple images of within-modality magnetic resonance data. It is shown that a superior denoising performance is obtained when (a) the interband covariances are fully accounted for and (b) prior models are used that better approximate the marginal distributions of the wavelet coefficients.     

自回归滤波器的研究

该文主要介绍了现代谱估计中常用到的自回归（AR）谱估计.利用Levinson-Durbin算法可以推导出在已知输出自相关序列的情况下确定预测误差滤波器系数,即AR模型的系数.AR模型的阶次选择是个关键问题,阶次太低会导致平滑的谱估计值,而阶次太高又会引起伪峰并且会产生一般的统计不稳定性.文章中采用了应用比较广泛的最终预测误差（FPE）准则和阿凯克信息论准则（AIC）,最终确定AR模型的阶数.并通过激励高斯白噪声仿真得到海洋混响的输出波形图.     

Joint segmentation of wind speed and direction using a hierarchical model

The problem of detecting changes in wind speed and direction is considered. Bayesian priors, with various degrees of certainty, are used to represent relationships between the two time series. Segmentation is then conducted using a hierarchical Bayesian model that accounts for correlations between the wind speed and direction. A Gibbs sampling strategy overcomes the computational complexity of the hierarchical model and is used to estimate the unknown parameters and hyperparameters. Extensions to other statistical models are also discussed. These models allow us to study other joint segmentation problems including segmentation of wave amplitude and direction. The performance of the proposed algorithms is illustrated with results obtained with synthetic and real data.     

Joint segmentation of wind speed and direction using a hierarchical model

The problem of detecting changes in wind speed and direction is considered. Bayesian priors, with various degrees of certainty, are used to represent relationships between the two time series. Segmentation is then conducted using a hierarchical Bayesian model that accounts for correlations between the wind speed and direction. A Gibbs sampling strategy overcomes the computational complexity of the hierarchical model and is used to estimate the unknown parameters and hyperparameters. Extensions to other statistical models are also discussed. These models allow us to study other joint segmentation problems including segmentation of wave amplitude and direction. The performance of the proposed algorithms is illustrated with results obtained with synthetic and real data.     

Variational Bayesian learning for robust AR modeling with the presence of sparse impulse noise

A single distribution is typically used to model the innovations of an autoregressive (AR) model. However, sparse impulses may exist within the innovations which may cause outliers in the observations. These impulses cannot be modeled by a single distribution and may potentially degrade the estimation. In this study, the innovation of an AR model is modeled by using both a Gaussian noise component and a sparse impulse noise model in order to obtain robust estimation and estimation of the impulses simultaneously. The Gaussian distribution models the normal noise and the sparse impulse noise model models the sparse abnormal innovation impulses. A hierarchal Bayesian model is built for the proposed model. Automatic relevance determination (ARD) priors are set for both the coefficients and the sparse impulses. A Variational Bayesian (VB) learning algorithm is given to estimate the parameters of the model. Experimental results show that the proposed model with the learning algorithm is valid for AR models with outliers caused by sparse innovation impulses, the coefficient estimation accuracy is better than other methods, and the sparse impulses can be estimated simultaneously.     

Recursive estimation for a noisy image represented by a hyperbolic PDE model

A recursive estimation technique is applied to the noisy image which is represented by a hyperbolic partial differential equation (PDE). Approximating a PDE model by a finite-difference approximation leads to an autoregressive (AR) model representation which Jain pointed out. In this paper, we use a new PDE model for the image representation. To apply a recursive estimation scheme to the image which is degraded by white noise, we propose the transformation of the.AR model into a state-space representation. To this representation, we apply a Kalman strip processor to reduce the order of the computation and storage, and the strip smoother (the optimal fixed-interval smoother) is also applied to obtain a better estimated imago. Three numerical examples are illustrated to show the effectiveness of the proposed algorithm.     

AR估计滤波误差能量最小二乘递推法

利用滤波误差能量给出了一个新的最小二乘快速递推算法。数值试验表明，该算法计算稳定性好，对噪声不敏感，能快速递推到高阶模型，并将该算法同Ｍａｒｐｌｅ算法等作了比较。     

A geometric view of conjugate priors

In Bayesian machine learning, conjugate priors are popular, mostly due to mathematical convenience. In this paper, we show that there are deeper reasons for choosing a conjugate prior. Specifically, we formulate the conjugate prior in the form of Bregman divergence and show that it is the inherent geometry of conjugate priors that makes them appropriate and intuitive. This geometric interpretation allows one to view the hyperparameters of conjugate priors as the effective sample points, thus providing additional intuition. We use this geometric understanding of conjugate priors to derive the hyperparameters and expression of the prior used to couple the generative and discriminative components of a hybrid model for semi-supervised learning.     

含噪声混沌信号最大Lyapunov指数计算

提出一种计算含噪声混沌序列最大Lyapunov指数的改进Rosentein算法,通过将原始含噪声的相空间与局部投影去噪后的相空间合并,使邻近点的选择更为准确,减小噪声的影响提高计算精度.分别对加入白噪声的Henon混沌序列和逐月太阳黑子混沌序列进行仿真,证明此方法有效性.     

修正的基于广义Gamma语音模型语音增强算法

广义Gamma模型是近年来新提出的一种语音分布模型,相对于传统的高斯或超高斯模型具有更好的普适性和灵活性,提出一种基于广义Gamma语音模型和语音存在概率修正的语音增强算法。在假设语音和噪声的幅度谱系数分别服从广义Gamma分布和Gaussian分布的基础上,推导了语音信号对数谱的最小均方误差估计式;在该模型下进一步推导了语音存在概率,对最小均方误差估计进行修正。仿真结果表明,与传统的短时谱估计算法相比,该算法不仅能够进一步提高增强语音的信噪比,而且可以有效减小增强语音的失真度,提高增强语音的主观感知质量。     

Dynamic models for nonstationary signal segmentation.

This paper investigates Hidden Markov Models (HMMs) in which the observations are generated from an autoregressive (AR) model. The overall model performs nonstationary spectral analysis and automatically segments a time series into discrete dynamic regimes. Because learning in HMMs is sensitive to initial conditions, we initialize the HMM model with parameters derived from a cluster analysis of Kalman filter coefficients. An important aspect of the Kalman filter implementation is that the state noise is estimated on-line. This allows for an initial estimation of AR parameters for each of the different dynamic regimes. These estimates are then fine-tuned with the HMM model. The method is demonstrated on a number of synthetic problems and on electroencephalogram data.     

基于递归神经网络的网络流量组合预测模型

为了提高网络流量的预测精度,提出了一种基于Elman递归神经网络,小波和自回归的网络流量组合预测模型.对流量时间序列进行小波分解,得到小波变换尺度系数序列和小波系数序列,对具有平稳特征的尺度系数序列用AR模型进行预测:而对体现了网络流量非线性、非平稳特性的小波系数序列使用Elman递归神经网络进行预测,最后通过Mallat算法重构得到网络流量的预测值.     

随机振动多窗口谱分析法模型建立及统计分析

针对随机振动中谱估计算法,分析了周期图估计算法对噪声系列的功率谱相关系数及加窗造成的信息损失,在此基础上分析了由直接谱估计算法构建的多窗口谱分析法,建立了其噪声模型,推导了估计方差减小与参与运算的窗口数的关系。针对白噪声序列,得到MTSA估计器避免加窗而造成信息损失时窗口数与信号序列的关系,最后推出了MTSA估计器的统计特征。     

Self-tuning weighted measurement fusion white noise deconvolution estimator and its convergence analysis

White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration, communication, signal processing, and state estimation. For the multisensor linear discrete time-invariant stochastic systems with correlated measurement noises, and with unknown ARMA model parameters and noise statistics, the on-line AR model parameter estimator based on the Recursive Instrumental Variable (RIV) algorithm, the on-line MA model parameter estimator based on Gevers–Wouters algorithm and the on-line noise statistic estimator by using the correlation method are presented. Using the Kalman filtering method, a self-tuning weighted measurement fusion white noise deconvolution estimator is presented based on the self-tuning Riccati equation. It is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steady-state white noise deconvolution estimator in a realization by using the dynamic error system analysis (DESA) method, so that it has the asymptotic global optimality. The simulation example for a 3-sensor system with the Bernoulli–Gaussian input white noise shows its effectiveness.     

基于抽取与重构的瞬时频率估计算法

研究了在AWGN信道中载波信号采样序列瞬时频率的概率密度分布模型,并通过假设检验验证该分布模型。分析了不同采样速率和信噪比对瞬时频率概率密度分布的影响,根据该分析结论提出了一种基于抽取与重构的瞬时频率的估计算法,并且对该算法的性能进行了详细的分析;还对多载波信号采样序列瞬时频率产生混叠以至无法分辨的情况进行分析,并推导了瞬时频率完全混叠时的极限公式。最后通过蒙特—卡罗仿真验证了提出的瞬时频率的概率密度分布的正确性。     

Approximate Predictive Densities and Their Applications in Generalized Linear Models

Exact calculations of model posterior probabilities or related quantities are often infeasible due to the analytical intractability of predictive densities. Here new approximations for obtaining predictive densities are proposed and contrasted with those based on the Laplace method. Our theory and a numerical study indicate that the proposed methods are easy to implement, computationally efficient, and accurate over a wide range of hyperparameters. In the context of GLMs, we show that they can be employed to facilitate the posterior computation under three general classes of informative priors on regression coefficients. A real example is provided to demonstrate the feasibility and usefulness of the proposed methods in a fully Bayes variable selection procedure.