Design of a fixed-point smoother based on an innovations theory for white gaussian plus coloured observation noise

The optimal fixed-point smoother is designed based on an innovations theory for the white gaussian plus coloured observation noise in linear continuous systems. The signals to be estimated are non-stationary or stationary stochastic processes. The proposed fixed-point smoothing algorithm calculates estimates sequentially by using the observed value, the autocovariance function of the signal plus the coloured observation noise process and the cross-covariance function of the signal with the observed value.     

Optimal non-linear estimation†

For the non-linear estimation problem with non-linear plant and observation models, white gaussian excitations and continuous data, the state-vector a posteriori probabilities for prediction and smoothing are obtained via the 'partition theorem'. Moreover, for the special class of non-linear estimation problems with linear models excited by white gaussian noise, and with non-gaussian initial state, explicit results are obtained for the a posteriori probabilities, the optimal estimates and the corresponding error-covariance matrices for filtering, prediction and smoothing. In addition, for the latter problem, approximate but simpler expressions are obtained by using a gaussian sum approximation of the initial state-vector probability density. As a special case of the above results, optimal linear smoothing algorithms are obtained in a new form.     

Non-linear smoothing algorithm for multi-dimensional dynamic systems

A new sub-optimum smoothing algorithm is presented for multi-dimensional dynamic systems. This algorithm is based upon quantization, multiple hypothesis testing, and the Viterbi decoding algorithm. The estimation of state vectors is carried out sequentially, component-by-component, and in parallel. A considerable memory reduction is achieved for state estimation implementation with the proposed algorithm. Simulation results, some of which are presented, show that the sub-optimum algorithm performs better than the extended Kalman filter algorithm for some non-linear multi-dimensional models with white gaussian disturbance and observation noises. In addition, the performance of the sub-optimum algorithm is almost as good as the Kalman filter algorithm for linear multi-dimensional models with white gaussian noise.     

On joint detection,estimation and system identification: discrete data case†

The recent results of Lainiotis (1971 a, b, 1971) on single-shot, as well as multishot, joint detection, estimation and system identification for continuous data and dynamics are extended to multishot, discrete data and discrete dynamical systems. The results are given for the signals generated by the linear dynamical systems with unknown parameter vectors and driven by white gaussian sequences, where the observation contains additive white gaussian noise. Specifically, it is shown that the above problem constitutes a class of non-linear mean-square estimation problems. By utilizing the adaptive approach, closed-form integral expressions are obtained for simultaneously optimal detection, estimation and system identification. In addition, several approximate algorithms that utilize linear Kalman estimators are presented to limit the storage requirement to finite size and reduce computational requirements. The results presented in this paper are applicable to both independent and Markov signalling sources     

一种基于小波变换图像去噪的方法

提出了一种基于图像软阈值小波变换的高斯白噪声消除法。该算法根据含噪声图的特点,把信号分成信号象素与可能噪声象素两类,对于可能是噪声的象素,采用图像的小波软阈值去噪方法进行滤波,而对信号象素不产生影响,且能保留更多的图像细节。文中也给出了标准中值滤波,自适应维纳滤波算法和小波软阈值去噪的算法进行比较实验,结果表明用小波软阈值去噪的算法处理高度污染高斯白噪声的图像能力明显强于标准中值滤波,稍微优于自适应维纳滤波算法,且能够比较好保留图像的细节部分。     

Robust ε-contaminated gaussian filtering of discrete-time linear systems

A robust slate estimation of multi-input single-output discrete-time linear systems is considered, where both the system disturbance and observation noise sequences contain outliers. The robust estimation problem is mathematically formulated for a special case assuming that the samples of the system disturbance and observation noise are from a known ε-contaminated gaussian density and a partially known ε-contaminated gaussian density, respectively. Through Monte Carlo simulations, the performance of the proposed robust filter is compared with that of the gaussian sum filter, which is the best non-linear filter when the densities of the underlying uncertainties are completely known. Comparison is also made between the proposed filter and some other available candidates.     

Estimation of kernel function of non-linear system by gaussian non-white noise

The kernel function of a non-linear system characterizes the properties of that system. The kernel function is well developed in the case of gaussian white noise. However in practice it is often necessary to apply an input of gaussian non-white noise in the control of biological systems. Although some methods have been developed that use gaussian non-white noise they do not have a simple computation. Furthermore, the kernel function obtained by these methods is not stable in practice. Here, we develop a gaussian non-white method based on a smoothing operation on the kernel function. The amplitude of the kernel function is then derived as a parameter, that characterizes the non-linear system. The kernel function obtained by a traditional method is compared by means of simulation with the smoothing method developed here.     

Robust Kalman filter for linear discrete-time system with gaussian sum noises

This paper considers the filtering problem for discrete-time linear systems where the distributions of the process and observation noises are of gaussian sum distributions. Since the gaussian sum noise can be considered to be a sample from one of the gaussian distributions forming the gaussian sum, we define the distribution selection parameters that specify sample noises from the gaussian sum distribution. By using the maximum a posteriori (MAP) estimates of the selection parameters, a robust state estimation algorithm combined with the Kalman filter is developed. Simulation studies are also included to show the effectiveness of the present algorithm.     

Equivalent discrete optimal control problem for randomly sampled digital control systems

This paper considers the transformation of the optimal digital control problem to en equivalent discrete-time optimal control problem in the case of deterministic and stochastic sampling. The continuous-time system to be controlled is linear and disturbed by additive continuous-time white noise (not necessarily gaussian). The observations available at the sampling instants are in general non-linear and corrupted by discrete-time noise independent of the system noise (not necessarily additive, white or gaussian). The performance criterion is quadratic and an integral rather than a sum.     

基于LDPC-OFDM技术的块均值视频水印算法

根据视频水印系统和通信系统的相似性,提出一种基于LDPC-OFDM的块均值视频水印算法。实验结果表明,该算法对视频质量影响小,可以很好地保证视频质量,实现水印的盲提取,且对高斯低通滤波、剪切攻击、高斯白噪声、椒盐噪声攻击及MPEG-2压缩、视频帧同步攻击具有较强的鲁棒性,是一种性能良好的盲视频水印算法。     

图像隐写与自然噪声辨识研究

提出一种辨识图像隐写与自然噪声的方法。从图像中常见的2类噪声(高斯白噪声和椒盐噪声)出发,基于加性噪声模型,利用图像直方图特征函数质点区分原始图像和隐写噪声图像,利用小波高频子带系数差分方差识别隐写图像与噪声图像。对大量隐写和噪声图像进行实验,结果表明,该方法可有效辨识图像隐写和噪声。     

Analytic expressions for rate and CV of a type I neuron driven by white gaussian noise

We study the one-dimensional normal form of a saddle-node system under the influence of additive gaussian white noise and a static "bias current" input parameter, a model that can be looked upon as the simplest version of a type I neuron with stochastic input. This is in contrast with the numerous studies devoted to the noise-driven leaky integrate-and-fire neuron. We focus on the firing rate and coefficient of variation (CV) of the interspike interval density, for which scaling relations with respect to the input parameter and noise intensity are derived. Quadrature formulas for rate and CV are numerically evaluated and compared to numerical simulations of the system and to various approximation formulas obtained in different limiting cases of the model. We also show that caution must be used to extend these results to the Theta neuron model with multiplicative gaussian white noise. The correspondence between the first passage time statistics for the saddle-node model and the Theta neuron model is obtained only in the Stratonovich interpretation of the stochastic Theta neuron model, while previous results have focused only on the Ito interpretation. The correct Stratonovich interpretation yields CVs that are still relatively high, although smaller than in the Ito interpretation; it also produces certain qualitative differences, especially at larger noise intensities. Our analysis provides useful relations for assessing the distance to threshold and the level of synaptic noise in real type I neurons from their firing statistics. We also briefly discuss the effect of finite boundaries (finite values of threshold and reset) on the firing statistics.     

一种自适应各项异性高斯滤波方法

为了提高图像的信噪比且尽可能保留图像边缘信息,论文提出了一种自适应各项异性高斯滤波方法,该方法根据各象素位置的灰度梯度值决定在这一点是采用各项同性还是各项异性高斯滤波,如果采用各项异性滤波,则由该处的灰度梯度方向角自适应决定各项异性滤波器的长轴方向。仿真实验表明,论文提出的自适应各项异性滤波器在边缘保持方面优于各项同性高斯滤波器。     

Optimum decoding-based smoothing algorithm for dynamic systems

A new smoothing algorithm for discrete models is presented. For the disturbance noise and the observation noise, only independency is assumed. Moreover the models’ functions are not limited to continuous functions, i.e. they can be non-continuous. This algorithm estimates the states by first quantizing them and then using the Viterbi decoding algorithm. Simulation results have shown that for some non-linear models the new algorithm performs better than the extended Kalman filter algorithm, while it performs almost as well as the Kalman filter algorithm for linear models with gaussian noise.     

A low-frequency gaussian white-noise generator†

The various methods of generating low-frequency noise are discussed. The merits of using a binary random signal, particularly the binary random square wave, as a noise source are considered, The advantages of applying the binary random signal to a low-pass filter to produce white gaussian noise are pointed out. A general method of designing filters which compensate for the fall in spectral response of the binary signal over the pass-band is described. Also, a theoretical method of determining the amplitude probability distribution of the filter output is described. The equations derived are solved for the case of third-order filters. Experimental and theoretical characteristics are given for the case of a noise generator using a third-order filter.     

Optimal non-linear estimation for distributed-parameter systems via the partition theorem

This paper considers the estimation problem for non-linear distributed-parameter systems via the ‘Partition Theorem’. First, the a posterioriprobability for the state is derived for the estimation of non-linear distributed-parameter systems. Secondly, linear systems excited by a white gaussian noise and with non-gaussian initial state are considered as a special class of the problem. The a posterioriprobability for the state, the optimal estimates and corresponding error covariance matrices are obtained by using the properties of the fundamental solution for the differential operator. Finally, it is shown that on approximate expression for the solution of the problem is also derived by applying a gaussian sum approximation technique.     

Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.     

基于双谱特征的同质量球形铀部件丰度检测

核部件属性检测是核材料检测中的热点与难点问题,针对铀部件检测系统中丰度信息易受探测器基本属性、几何位置及噪声的影响,通过分析铀部件探测信号互相关函数的双谱特性,提取双谱中的特征量作为铀部件丰度检测的数据集,消除了本底噪声对探测信号的影响。此外,基于BP神经网络,构建了一种同质量球形铀部件的丰度判定方法,实现了对测试样本的丰度检测。测试结果表明,该方法在存在高斯白噪声情况下可有效判定同质量球形铀部件的丰度,其测试误差的平均值为0.005115,最大误差为0.009927。     

The effect of noise on edge orientation computations

This paper studies the effect of image noise on edge orientation computations. It is found that noise affects estimation of edge orientation in a complex way, but this is simplified for those ‘circular’ operators which act in a strictly vectorial manner. In that case the distribution of edge orientations is closely gaussian for gaussian image noise. These results have important consequences for object location schemes based on the generalised Hough transform - especially when noise is high or contrast is low. Suprisingly, the consequences are much less serious with impulse noise.     

Determination of firing times for the stochastic Fitzhugh-Nagumo neuronal model

We present for the first time an analytical approach for determining the time of firing of multicomponent nonlinear stochastic neuronal models. We apply the theory of first exit times for Markov processes to the Fitzhugh-Nagumo system with a constant mean gaussian white noise input, representing stochastic excitation and inhibition. Partial differential equations are obtained for the moments of the time to first spike. The observation that the recovery variable barely changes in the prespike trajectory leads to an accurate one-dimensional approximation. For the moments of the time to reach threshold, this leads to ordinary differential equations that may be easily solved. Several analytical approaches are explored that involve perturbation expansions for large and small values of the noise parameter. For ranges of the parameters appropriate for these asymptotic methods, the perturbation solutions are used to establish the validity of the one-dimensional approximation for both small and large values of the noise parameter. Additional verification is obtained with the excellent agreement between the mean and variance of the firing time found by numerical solution of the differential equations for the one-dimensional approximation and those obtained by simulation of the solutions of the model stochastic differential equations. Such agreement extends to intermediate values of the noise parameter. For the mean time to threshold, we find maxima at small noise values that constitute a form of stochastic resonance. We also investigate the dependence of the mean firing time on the initial values of the voltage and recovery variables when the input current has zero mean.