Variational Bayesian inference based robust multiple measurement sparse signal recovery

This work concentrates on not only probing into a novel Bayesian probabilistic model to formulate a general type of robust multiple measurement vectors sparse signal recovery problem with impulsive noise, but also developing an improved variational Bayesian method to recover the original joint row sparse signals. In the design of the model, two three-level hierarchical Bayesian estimation procedures are designed to characterize impulsive noise and joint row sparse source signals by means of Gaussian scale mixtures and multivariate generalized t distribution. Those hidden variables, included in signal and measurement models are estimated based on a variational Bayesian framework, in which multiple kinds of probability distributions are adopted to express their features. In the design of the algorithm, the proposed algorithm is a full Bayesian inference approach related to variational Bayesian estimation. It is robust to impulsive noise, since the posterior distribution estimation can be effectively approached through estimating unknown parameters. Extensive simulation results show that the proposed algorithm significantly outperforms the compared robust sparse signal recovery approaches under different kinds of impulsive noises.     

Sparse kernel density estimations and its application in variable selection based on quadratic Renyi entropy

A novel sparse kernel density estimation method is proposed based on the sparse Bayesian learning with random iterative dictionary preprocessing. Using empirical cumulative distribution function as the response vectors, the sparse weights of density estimation are estimated by sparse Bayesian learning. The proposed iterative dictionary learning algorithm is used to reduce the number of kernel computations, which is an essential step of the sparse Bayesian learning. With the sparse kernel density estimation, the quadratic Renyi entropy based normalized mutual information feature selection method is proposed. The simulation of three examples demonstrates that the proposed method is comparable to the typical Parzen kernel density estimations. And compared with other state-of-art sparse kernel density estimations, our method also has a shown very good performance as to the number of kernels required in density estimation. For the last example, the Friedman data and Housing data are used to show the property of the proposed feature variables selection method.     

基于因果影响独立模型的贝叶斯网络参数学习

基于因果影响独立模型及其中形成的特定上下文独立关系,提出一种适于样本学习的贝叶斯网络参数学习算法。该算法在对局部概率模型降维分解的基础上,通过单父节点条件下的子节点概率分布来合成局部结构的条件概率分布,参数定义复杂度较低且能较好地处理稀疏结构样本集。实验结果表明,该算法与标准最大似然估计算法相比,能充分利用样本信息,具有较好的学习精度。     

基于带有噪声输入的稀疏高斯过程的人体姿态估计

高斯过程回归（Gaussian process regression，GPR）是一种广泛应用的回归方法，可以用于解决输入输出均为多元变量的人体姿态估计问题.计算复杂度是高斯过程回归的一个重要考虑因素，而常用的降低计算复杂度的方法为稀疏表示算法.在稀疏算法中，完全独立训练条件（Fully independent training conditional，FITC）法是一种较为先进的算法，多用于解决输入变量彼此之间完全独立的回归问题.另外，输入变量的噪声问题是高斯过程回归的另一个需要考虑的重要因素.对于测试的输入变量噪声，可以通过矩匹配的方法进行解决，而训练输入样本的噪声则可通过将其转换为输出噪声的方法进行解决，从而得到更高的计算精度.本文基于以上算法，提出一种基于噪声输入的稀疏高斯算法，同时将其应用于解决人体姿态估计问题.本文实验中的数据集来源于之前的众多研究人员，其输入为从视频序列中截取的图像或通过特征提取得到的图像信息，输出为三维的人体姿态.与其他算法相比，本文的算法在准确性，运行时间与算法稳定性方面均达到了令人满意的效果.     

Graphical model based continuous estimation of distribution algorithm

In this paper, a new estimation of distribution algorithm is introduced. The goal is to propose a method that avoids complex approximations of learning a probabilistic graphical model and considers multivariate dependencies between continuous random variables. A parallel model of some subgraphs with a smaller number of variables is learned as the probabilistic graphical model. In each generation, the joint probability distribution of the selected solutions is estimated using a Gaussian Mixture model. Then, learning the graphical model of dependencies among random variables and sampling are done separately for each Gaussian component. In the learning step, using the selected solutions of each Gaussian mixture component, the structure of a Markov network is learned. This network is decomposed to maximal cliques and a clique graph. Then, complete Bayesian network structures are learned for these subgraphs using an optimization algorithm. The proposed optimization problem is a 0–1 constrained quadratic programming which finds the best permutation of variables. Then, sampling is done from each Bayesian network of each Gaussian component. The introduced method is compared with the other network-based estimation of distribution algorithms for optimization of continuous numerical functions.     

Bayesian estimation for homogeneous and inhomogeneous Gaussianrandom fields

This paper investigates Bayesian estimation for Gaussian Markov random fields. In particular, a new class of compound model is proposed which describes the observed intensities using an inhomogeneous model and the degree of spatial variation described by a second random field. The coupled Markov random fields are used as prior distributions, and combined with Gaussian noise models to produce posterior distributions on which estimation is based. All model parameters are estimated, in a fully Bayesian setting, using the Metropolis-Hasting algorithm. The full posterior estimation procedures are illustrated and compared using various artificial examples. For these examples the inhomogeneous model performs very favorably when compared to the homogeneous model, allowing differential degrees of smoothing and varying local textures     

强脉冲噪声环境下的多径衰信道估计

提出一种在强干扰脉冲噪声存在下对无线多径信道进行估计的算法.在无线通信系统中,衰落信道可以采用自回归(AR)模型建模,通过RLS算法和自适应Kalman滤波器分别对AR模型的参数进行估计,但是,这两种算法对噪声干扰非常敏感.为了加快RLS算法的收敛性,并有效抑制大脉冲干扰的影响,在算法的改进中引入了抑制因子,用于对脉冲干扰幅度的抑制.仿真结果显示:相比于传统的算法,改进后的算法在联合估计信道时,提高了抵抗大脉冲干扰的能力,加快了待估参数的收敛速度.     

基于广义最大Versoria准则的稀疏自适应滤波算法

针对脉冲噪声干扰环境下传统稀疏自适应滤波稳态性能差,甚至无法收敛等问题,同时为提高稀疏参数辨识的精度的同时不增加过多计算代价,提出了一种基于广义最大Versoria准则（GMVC）的稀疏自适应滤波算法——带有CIM约束的GMVC（CIMGMVC）。首先,利用广义Versoria函数作为学习准则,其包含误差p阶矩的倒数形式,当脉冲干扰出现导致误差非常大时,GMVC将趋近于0,从而达到抑制脉冲噪声的目的。其次,将互相关熵诱导维度（CIM）作为稀疏惩罚约束和GMVC相结合来构建新代价函数,其中的CIM以高斯概率密度函数为基础,当选择合适核宽度时,可无限逼近于l_{\mathrm{0}}-范数。最后,应用梯度法推导出CIMGMVC算法,并分析了所提算法的均方收敛性。在Matlab平台上采用\alpha-stable分布模型产生脉冲噪声进行仿真,实验结果表明所提出的CIMGMVC算法能有效地抑制非高斯脉冲噪声的干扰,在稳健性方面优于传统稀疏自适应滤波,且稳态误差低于GMVC算法。     

Bayesian sparse solutions to linear inverse problems with non-stationary noise with Student-t priors

Bayesian approach has become a commonly used method for inverse problems arising in signal and image processing. One of the main advantages of the Bayesian approach is the possibility to propose unsupervised methods where the likelihood and prior model parameters can be estimated jointly with the main unknowns. In this paper, we propose to consider linear inverse problems in which the noise may be non-stationary and where we are looking for a sparse solution. To consider both of these requirements, we propose to use Student-t prior model both for the noise of the forward model and the unknown signal or image. The main interest of the Student-t prior model is its Infinite Gaussian Scale Mixture (IGSM) property. Using the resulted hierarchical prior models we obtain a joint posterior probability distribution of the unknowns of interest (input signal or image) and their associated hidden variables. To be able to propose practical methods, we use either a Joint Maximum A Posteriori (JMAP) estimator or an appropriate Variational Bayesian Approximation (VBA) technique to compute the Posterior Mean (PM) values. The proposed method is applied in many inverse problems such as deconvolution, image restoration and computed tomography. In this paper, we show only some results in signal deconvolution and in periodic components estimation of some biological signals related to circadian clock dynamics for cancer studies.     

An Interacting Multiple Model Approach for State Estimation with Non‐Gaussian Noise Using a Variational Bayesian Method

The conventional interacting multiple models (IMM) approach for a hybrid system under the Gaussian assumption is limited for most real applications due to the noisy measurements often being in the presence of outliers. This paper aims at accommodating the IMM approach to the non‐Gaussian cases where outliers exist. In the proposed IMM algorithm, the Student‐t distribution is used to model the non‐Gaussian measurement noise. At the interaction step, the mixed statistics of the noise parameter under a Bayesian framework are obtained via a Gamma approximation and a recently reported moments matching method. To address the state noise‐coupled intractability in Bayesian filtering, a variational Bayesian method is utilized to approximate the posterior distributions of the noise and state recursively. The proposed algorithm is tested with a maneuvering target tracking example and is shown to be robust to the outliers.     

基于高斯-柯西混合模型的单幅散焦图像深度恢复方法

单幅图像场景深度的获取一直是计算机视觉领域的一个难题。使用高斯分布函数或柯西分布函数近似点扩散函数模型(PSF),再根据图像边缘处散焦模糊量的大小与场景深度之间的关系估算出深度信息,是一种常用的方法。真实世界中图像模糊的缘由千变万化,高斯分布函数以及柯西分布函数并不一定是最佳的近似模型,并且传统的方法对于图像存在阴影、边缘不明显以及深度变化比较细微的区域的深度恢复结果不够准确。为了提取更为精确的深度信息,提出一种利用高斯-柯西混合模型近似PSF的方法;然后对散焦图像进行再模糊处理,得到两幅散焦程度不同的图像;再通过计算两幅散焦图像边缘处梯度的比值估算出图像边缘处的散焦模糊量,从而得到稀疏深度图;最后使用深度扩展法得到场景的全景深度图。通过大量真实图像的测试,说明新方法能够从单幅散焦图像中恢复出完整、可靠的深度信息,并且其结果优于目前常用的两种方法。     

Robust 1-bit compressive sensing via variational Bayesian algorithm

In a compressive sensing (CS) framework, a sparse signal can be stably reconstructed at a reduced sampling rate. Quantization and noise corruption are inevitable in practical applications. Recent studies have shown that using only the sign information of measurements can achieve accurate signal reconstruction in a CS framework. We consider the problem of reconstructing a sparse signal from 1-bit quantized, Gaussian noise corrupted measurements. In this paper, we present a variational Bayesian inference based 1-bit compressive sensing algorithm, which essentially models the effect of quantization as well as the Gaussian noise. A variational message passing method is adopted to achieve the inference. Through numerical experiments, we demonstrate that our algorithm outperforms state-of-the-art 1-bit compressive sensing algorithms in the presence of Gaussian noise corruption.     

基于不确定模型误差系统的变分贝叶斯STCKF

强跟踪容积卡尔曼滤波器在对含有模型误差和时变噪声的非线性系统进行滤波时, 容易出现性能降低甚至发散. 鉴于此, 提出一种基于变分贝叶斯的强跟踪容积卡尔曼滤波算法. 该算法运用虚拟噪声法补偿模型误差, 假设虚拟噪声均值非零, 且满足高斯分布, 虚拟噪声方差服从逆gamma分布, 在强跟踪容积卡尔曼滤波器估计状态的同时, 采用变分贝叶斯推理估计虚拟噪声参数. 仿真结果表明, 所提出算法对含模型误差与时变噪声的非线性系统具有较好的估计精度, 相比于自适应算法具有更强的鲁棒性.     

基于变分贝叶斯推断的字典学习算法

传统的字典学习算法在对训练图像进行学习时收敛速率慢,当图像受到噪声干扰时学习效果变差.对此,提出一种基于变分推断的字典学习算法.首先设定模型中各参数的共轭稀疏先验分布;然后基于贝叶斯网络求出所有参数的联合概率密度函数;最后利用变分贝叶斯推断原理计算出各参数的最优边缘分布,训练出自适应学习字典.利用该字典进行图像去噪实验以及压缩感知重构实验,仿真结果表明,所提出的算法可显著提高字典学习效率,对测试图像的去噪效果和重构精度有很大改善.     

导向矢量失配情况下基于稀疏表示的波达方向估计算法

提出了一种传感器阵列导向矢量失配情况下的基于稀疏表示的信号源波达方向DOA估计算法。针对一些实际环境中噪声重尾现象严重的特点,采用合成圆对称广义高斯噪声分布对其进行模拟。考虑到实际环境中传感器自身运动以及外界环境因素的改变可能会导致传感器导向矢量产生波动,利用加权最小二乘法对波动生成的增益值进行最优估计。然后,构建信号模型的分数低阶矩FLOM矩阵,进行矢量化处理,以提高其数组维数。最后,利用稀疏表示方法重构信号模型,将信号源DOA估计转化为二阶锥规划问题进行求解,并采用奇异值分解降低运算量。仿真结果表明,本算法的信号源DOA估计具有很高的分辨率,且有效地避免了导向矢量失配对DOA估计产生的影响。     

HMM-Based Gain Modeling for Enhancement of Speech in Noise

Accurate modeling and estimation of speech and noise gains facilitate good performance of speech enhancement methods using data-driven prior models. In this paper, we propose a hidden Markov model (HMM)-based speech enhancement method using explicit gain modeling. Through the introduction of stochastic gain variables, energy variation in both speech and noise is explicitly modeled in a unified framework. The speech gain models the energy variations of the speech phones, typically due to differences in pronunciation and/or different vocalizations of individual speakers. The noise gain helps to improve the tracking of the time-varying energy of nonstationary noise. The expectation-maximization (EM) algorithm is used to perform offline estimation of the time-invariant model parameters. The time-varying model parameters are estimated online using the recursive EM algorithm. The proposed gain modeling techniques are applied to a novel Bayesian speech estimator, and the performance of the proposed enhancement method is evaluated through objective and subjective tests. The experimental results confirm the advantage of explicit gain modeling, particularly for nonstationary noise sources     

稀疏视觉SLAM对平面激光雷达传感的稠密化模拟

为了解决稀疏特征点VSLAM （visual simultaneous localization and mapping）由于其构图稀疏性,在视觉导航应用方面的短板,提出一种高斯滤波插值的方法对其特征点进行稠密化处理,实现对平面激光雷达反馈的模拟.本文利用高斯分布以及迭代滤波实现数据的稠密化,通过建立全局高斯滤波以及局部高斯分布估计,实现对稀疏VSLAM空间点平面投影的数据插补,进而实现对平面激光雷达数据的模拟.仅使用CPU情况下,算法每帧耗时为0.0003s~0.006s,插值结果相对误差为7.956%.实验证明,该插值方法成功实现了稀疏投影点的稠密化,插补结果与真实激光雷达反馈相似度高,为视觉导航提供了一种有效的前端传感处理方法.     

具有噪声信息与状态模型不确定系统的IMM自适应滤波

卡尔曼滤波器广泛用于解决线性高斯系统的状态估计问题.然而,在实际应用中过程噪声和系统模型参数先验信息未知,且量测受到异常值干扰,给准确估计系统状态带来极大困难.针对具有噪声信息和状态模型不确定的动态系统,提出一种广义交互式多模型自适应滤波算法.该算法设计多个模型并行的方式对系统不确定进行处理,对于每个模型,建立Skew-T分布非对称重尾噪声表示模型,为了解决过程噪声与系统协方差相互耦合难以求解的问题,利用逆威沙特分布对系统预测协方差矩阵进行描述,并通过变分贝叶斯推理递归计算系统状态的后验分布.仿真结果和实验验证表明,在噪声信息和状态模型不确定条件下,所提出算法具有较高的估计精度.     

基于自然图像块相似性和稀疏先验性的图像复原

针对物体成像过程受光学系统散焦、运动、大气扰动及光电噪声等因素影响,导致光学系统获取的图像存在噪声、模糊、畸变等降质问题,对基于自然图像块相似性和自然图像稀疏先验信息的图像复原方法进行研究,提出一种泛化的基于图像块相似性和自然图像稀疏先验的图像复原框架。首先,在研究自然图像稀疏先验模型的基础上比较了几种图像块的相似性模型,比较结果表明在图像复原中利用图像块的高相似性先验条件模型能够提升图像复原的性能;接着,构建和优化了基于图像块的期望log相似性模型,减少了运行时间,简化了学习过程;最后,通过构建一种近似的最大后验估计（MAP）算法,最终实现了基于优化的期望块log相似性和混合高斯模型（GMM）的图像复原。仿真实验结果表明,所提方法能够很好地复原包含有各种模糊和加性噪声的退化图像,所得图像的峰值信噪比（PSNR）和结构相似度（SSIM）都优于当前技术条件下的其他稀疏先验复原方法,并具有更好的视觉效果。     

基于多元混合高斯分布的多分类人脸识别方法

针对实际人脸图像含有的噪声模型常常表现出的非高斯特性, 该非高斯特性具有较厚重的拖尾现象, 提出一种基于多元混合高斯分布的多分类人脸识别方法。该方法将多元混合高斯分布、核函数、概率密度函数估计中的参数估计以及贝叶斯理论结合起来, 能对含有重尾噪声的人脸图像有较高的识别率。用ORL标准人脸库进行验证, 实验结果表明了可行性。