Monte Carlo smoothing with application to audio signal enhancement

We describe methods for applying Monte Carlo filtering and smoothing for estimation of unobserved states in a nonlinear state-space model. By exploiting the statistical structure of the model, we develop a Rao-Blackwellized particle smoother. Due to the lengthy nature of real signals, we suggest processing the data in blocks, and a block-based smoother algorithm is developed for this purpose. All the algorithms suggested are tested with real speech and audio data, and the results are shown and compared with those generated using the generic particle smoother and the extended Kalman filter (EKF). It is found that the proposed Rao-Blackwellized particle smoother improves on the standard particle smoother and the extended Kalman smoother. In addition, the proposed block-based smoother algorithm enhances the efficiency of the proposed Rao-Blackwellized smoother by significantly reducing the storage capacity required for the particle information     

带相关噪声的观测融合稳态Kalman滤波算法及其全局最优性

对于带相关的输入白噪声和观测白噪声及相关观测白噪声的多传感器线性离散定常随机系统,用加权最小二乘(WLS)法提出了一种加权观测融合稳态Kalman滤波算法,可处理状态、白噪声和信号融合滤波、平滑、预报问题。基于稳态信息滤波器证明了它完全功能等价于集中式观测融合稳态Kalman滤波算法,因而它具有渐近全局最优性,且可减少计算负担。一个跟踪系统仿真例子验证了它的功能等价性。     

多目标跟踪的多伯努利平滑方法

为提高基于滤波的多目标跟踪方法的性能,提出了一种多伯努利平滑方法.该方法由前向滤波和反向平滑两部分组成,前向滤波采用势平衡多目标多伯努利滤波,反向平滑利用多伯努利概率密度近似多目标平滑状态的概率密度,实现多目标平滑状态概率密度的反向递推计算.仿真结果表明,与滤波相比,多伯努利平滑对目标数量和目标状态的估计精度都有显著提高.     

A new image smoothing method based on a simple model of spatialprocessing in the early stages of human vision

The difficulty of preserving edges is central to the problem of smoothing images. The main problem is that of distinguishing between meaningful contours and noise, so that the image can be smoothed without loss of details. Substantial efforts have been devoted to solving this difficult problem, and a plethora of filtering methods have been proposed in the literature. Non-linear filters have proved to be more efficient than their linear counterparts. Here, a new nonlinear filter for noise smoothing is introduced. This filter is based on the psychophysical phenomenon of human visual contrast sensitivity. Results on real images are presented to demonstrate the validity of our approach compared to other known filtering methods.     

容积Rauch-Tung-Striebel平滑器

针对离散非线性系统的状态平滑问题,基于Rauch-Tung-Striebel(RTS)理论设计了一种容积卡尔曼平滑器(Cubature Kalman Smoother,CKS),即容积Rauch-Tung-Striebel平滑器(RTSCKS)。首先,基于经典贝叶斯状态估计理论框架,推导了状态概率密度分布形式的非线性系统最优平滑算法;其次,基于Rauch-Tung-Striebel理论,建立了相应的最优平滑递推算法;然后,将其与容积卡尔曼滤波算法相结合,建立了递推形式的RTS-CKS平滑器;最后,通过典型的纯方位跟踪模型验证了该平滑器的可行性和有效性。该平滑器为非线性系统的状态估计提供了新的估计算法。     

基于均值漂移的自适应滤波及其在光谱信号处理中的应用

该文给出了一种基于均值漂移的自适应双边滤波方法,其性能仅取决于空域的核尺度参数,幅度域的核尺度是根据信号的局部特征自适应选取的。该方法能够去除脉冲噪声,能有效抑制非脉冲噪声,并有较强的边缘保护能力。实验和分析表明本文方法的整体性能优于高斯滤波和中值滤波。该文将所提出方法用于天体光谱的去噪,并与均值漂移滤波和小波硬阈值法进行了比较,结果表明:该方法能够有效抑制光谱中天光背景噪声和随机噪声,并能较好地保护谱线信息,更适于天体光谱信号的处理。     

数字图像中值滤波技术研究

中值滤波作为图像处理中的一种非线性滤波技术,在有效抑制脉冲噪声的同时能很好地保护图像信号的细节信息,尤其是在处理椒盐噪声方面效果较好,得到了广泛的研究和应用。文章通过对中值滤波及其改进方法的研究,比较了不同方法的运算效率及对不同图像的去噪效果,分析中值滤波技术的研究方向。     

The$H_infty$Fixed-Interval Smoothing Problem for Continuous Systems

The$H_infty$smoothing problem for continuous systems is treated in a state space representation by means of variational calculus techniques. The smoothing problem is introduced in an$H_infty$criterion by means of an artificial discontinuity that splits the problem in term of$H_infty$forward and$H_infty$backward filtering problems. Hence, the smoother design is realized in three steps. First, a forward filter is developed. Secondly, a backward filter is developed taking into account the backward Markovian model. The third step consists of combining the two previous steps in order to compute the$H_infty$smoothed estimate. An example shows the efficiency of this proposed smoother.     

Nonlinear filters for linear models (a robust approach)

We consider the altering problem for linear models where the driving noises may be quite general, nonwhite and non-Gaussian, and where the observation noise may only be known to belong to a finite family of possible disturbances. Using diffusion approximation methods, we show that a certain nonlinear filter minimizes the asymptotic filter variance. This nonlinear filter is obtained by choosing at each moment, on the basis of the observations, one of a finite number of Kalman-type filters driven by a suitable nonlinear transformation of the “innovations”. As a byproduct we obtain also the asymptotic identification of the a priori unknown observation noise disturbance. By yielding an asymptotically efficient filter in face of an unknown observation noise, our approach may also be viewed as a robust approach to filtering for linear models     

A new iterated two-band diffusion equation:theory and its application

We propose an iterated two-band filtering method to solve the selective image smoothing problem. We prove that a discrete computation step in an iterated nonlinear diffusion-based filtering algorithm is equivalent to a sequence of operations, including decomposition, regularization, and then reconstruction, in the proposed two-band filtering scheme. To correctly separate the high frequency components from the low frequency ones in the decomposition process, we adopt a dyadic wavelet-based approximation scheme. In the regularization process, we use a diffusivity function as a guide to retain useful data and suppress noises. Finally, the signal of the next stage, which is a "smoother" version of the signal at the previous stage, can be computed by reconstructing the decomposed low frequency component and the regularized high frequency component. Based on the proposed scheme, the smoothing operation can be applied to the correct targets. Experimental results show that our new approach is really efficient in noise removing.     

Smoothing of discontinuous signals: the competitive approach

Discontinuous signals buried in noise cannot be recovered by linear filtering methods. This paper presents a new class of nonlinear filters in which sets of forward and backward linear predictors and smoothers compete with each other at each timestep. The winner of each competition is granted the right to produce the smoothed estimate at that timestep. This conceptually simple approach to nonlinear filtering, called the competitive smoothing approach, is justified by considering sets of Kalman filters (corresponding to the hypotheses used in the Bayesian framework) which are used to derive model credibility coefficients. These are shown to essentially “switch” between the various models. We argue that the concept of competitive smoothing is considerably more general than just the Kalman setting, and can be used with almost any predictors and/or smoothers. Several examples are presented which demonstrate the efficacy of the approach at both smoothing and preserving jump discontinuities. Comparisons are made with the other main nonlinear filtering approach, the median filter     

自适应LUM滤波器

低-高-中滤波器(Lower-upper-middlefilter,简称LUM滤波器)是中值滤波基础上发展起来的一种非线性滤波器.提出了一种改进的LUM滤波器的算法.算法对LUM滤波器进行了两方面的改进:一方面针对未被噪声污染的非边缘区域,不滤波;另一方面自动查找LUM滤波器锐化窗口的位置.与原有的LUM滤波器相比,它能缩短程序运行的时间,较好地降噪,保护图像的有用信息,更好地增强图像的边缘.     

多传感器最优信息融合白噪声反卷积滤波器

基于Kalman滤波方法和白噪声估计理论,在线性最小方差按矩阵加权最优信息融合准则下,提出了带相关噪声系统多传感器信息融合白噪声反卷积滤波器.提出了各传感器滤波误差之间的协方差阵计算公式,可用于计算最优融合加权阵.同单传感器情形相比,可提高融合滤波精度.它可减少在线计算负担,便于实时应用.它可应用于石油地震勘探信号处理.一个3传感器信息融合Bernoulli-Gaussian白噪声反卷积滤波器的仿真例子说明了其有效性.     

Time-variant forward-backward FIR denoising of piecewise-smooth signals

We address a novel time-variant forward-backward (FB) unbiased finite impulse response (UFIR) smoothing algorithm designed to denoise piecewise-smooth signals with known or well detectable edge positions. Owing to the variable averaging interval, the algorithm unites advantages of linear structures with robustness of nonlinear ones. The FB UFIR smoother has been examined in Gaussian and heavy-tailed noise environments and compared to the nonlinear myriad filter derived under the Cauchy statistics. We show that the solution proposed is able to preserve edges without jitter and provide efficient denoising with sufficient robustness against outliers and noise heavy tails.     

基于改进的各向异性SUSAN算法的MEMS微结构图像滤波

为了改善在滤除微机电系统微结构图像的噪声时导致边缘模糊的问题,提出了一种改进的各向异性SUSAN滤波算法。该方法用独立强度传播模型决定长短轴的方差,由该点的梯度方向决定滤波器的长轴方向,由局部图像的灰度值与核值的差构成的局部均值构成SUSAN滤波器的自适应阈值,从而构建出各向异性SUSAN滤波器。该算法在平滑图像同时能保持图像的边缘特征。结果表明,各向异性SUSAN滤波器能够很好地降噪并保持图像的边缘信息。     

复合滤波在三维电子罗盘输出数据处理中的应用

三维电子罗盘在长距离数据传输过程中,将受到外界噪声的干扰。该噪声不仅含有高斯噪声,还含有脉冲噪声。介绍一种抑制噪声干扰的复合数据滤波方法,即先利用一种非线性滤波器——中值滤波器,消除脉冲噪声,然后再利用FIR低通滤波器,对其进行平滑处理。与传统的直接采用线性滤波器的滤波结果相比较,该方法的滤波效果更为理想。     

基于几何模型的SAR图像斑点噪声的抑制

斑点噪声的抑制一直是合成孔径雷达(SAR)图像处理的重要研究课题。本文利用几何模型对合成孔径雷达图像进行滤波。通过对几何模型除噪性能进行分析,提出了一个数值计算的改进格式。新的迭代格式能较好地保留图像的边缘、尖点和细节信息。最后对合成孔径雷达图像进行去噪实验,与小波阈值除噪、Lee滤波进行比较具有更好的滤波效果。     

Detection and extraction of periodic noises in audio and biomedical signals using Kalman filter

This paper studies the subject of adaptive noise cancelation using the Kalman filtering technique to achieve high precision and fast convergence. It is shown that the Kalman filter can successfully be designed to detect and extract periodic noises which may be constituted of different sinusoidal components with possibly unknown and/or time-varying frequencies. This highlights the feature of Kalman filter in synthesizing periodic noises in the time-domain which is not possible using Fourier-based methods such as DFT. Usefulness of the method is discussed in the context of two examples: active cancelation of periodic noises from audio waveforms and filtering of electrocardiogram measurements.     

Robust frequency-selective filtering using weighted myriad filtersadmitting real-valued weights

Weighted myriad smoothers have been proposed as a class of nonlinear filters for robust non-Gaussian signal processing in impulsive noise environments. However, weighted myriad smoothers are severely limited since their weights are restricted to be non-negative. This constraint makes them unusable in bandpass or highpass filtering applications that require negative filter weights. Further, they are incapable of amplifying selected frequency components of an input signal. In this paper, we generalize the weighted myriad smoother to a richer structure: a weighted myriad filter admitting real-valued weights. This involves assigning a pair of filter weights (one positive and the other negative) to each of the input samples. Equivalently, the filter can be described as a weighted myriad smoother applied to a transformed set of samples that includes the original input samples as well as their negatives. The weighted myriad filter is analogous to a normalized linear FIR filter with real-valued weights whose absolute values sum to unity. By suitably scaling the output of the weighted myriad filter, we extend it to yield the so-called scaled weighted myriad filter, which includes (but is more powerful than) the traditional unconstrained linear FIR filter. Finally we derive stochastic gradient-based nonlinear adaptive algorithms for the optimization of these novel myriad filters under the mean square error criterion