Singular spectrum analysis and Fisher–Shannon analysis of spring flow time series: An application to Anjar Spring,Lebanon

In this study, the time dynamics of water flow from Anjar Spring was investigated, which is one of the major issuing springs in the central part of Lebanon. Likewise, many water sources in Lebanon, this spring has no continuous records for the discharge, and this would prevent the application of standard time series analysis tools. Furthermore, the highly nonstationary character of the series implies that suited methodologies can be employed to get insight into its dynamical features. Therefore, the Singular Spectrum Analysis (SSA) and Fisher–Shannon (FS) method, which are useful methods to disclose dynamical features in noisy nonstationary time series with gaps, are jointly applied to analyze the Anjar Spring water flow series. The SSA revealed that the series can be considered as the superposition of meteo-climatic periodic components, low-frequency trend and noise-like high-frequency fluctuations. The FS method allowed to extract and to identify among all the SSA reconstructed components the long-term trend of the series. The long-term trend is characterized by higher Fisher Information Measure (FIM) and lower Shannon entropy, and thus, represents the main informative component of the whole series. Generally water discharge time series presents very complex time structure, therefore the joint application of the SSA and the FS method would be very useful in disclosing the main informative part of such kind of data series in the view of existing climatic variability and/or anthropogenic challenges.     

Application of permutation entropy method in the analysis of chaotic,noisy, and chaotic noisy series

We have considered a permutation entropy method for analyzing chaotic, noisy, and chaotic noisy series. We have introduced the concept of permutation entropy from a survey of some features of information entropy (Shannon entropy), described the algorithm for its calculation, and indicated the advantages of this approach in the analysis of time series; the application of this method in the analysis of various model systems and experimental data has also been demonstrated.     

奇异谱分析用于提升双光梳激光测距精度

从含噪数据中提取信号从而提升数据采集系统精度是极为重要的问题.奇异谱分析(singular spectrum analysis,SSA)作为一种无参数频谱估计技术,广泛用于区分系统模型未知情况下的动态系统信号的复杂成分.本文应用SSA方法提取双光梳飞秒激光测距系统中的含噪时间序列的距离信息,数值仿真显示SSA方法可以从含有有色噪声的信号中提取距离信号.实验中,SSA方法成功地从含有量子噪声的测距信号中提取出激光与目标之间的距离信息,提取后的信号有13倍的精度提升.这种方法同样适用于高维信号,如基于飞秒激光测距的高精度、高速率表面形貌测量的图像提取.     

The application of neural networks to forecast fuzzy time series

Fuzzy time series models have been applied to handle nonlinear problems. To forecast fuzzy time series, this study applies a backpropagation neural network because of its nonlinear structures. We propose two models: a basic model using a neural network approach to forecast all of the observations, and a hybrid model consisting of a neural network approach to forecast the known patterns as well as a simple method to forecast the unknown patterns. The stock index in Taiwan for the years 1991–2003 is chosen as the forecasting target. The empirical results show that the hybrid model outperforms both the basic and a conventional fuzzy time series models.     

A new complexity measure for time series analysis and classification

Complexity measures are used in a number of applications including extraction of information from data such as ecological time series, detection of non-random structure in biomedical signals, testing of random number generators, language recognition and authorship attribution etc. Different complexity measures proposed in the literature like Shannon entropy, Relative entropy, Lempel-Ziv, Kolmogrov and Algorithmic complexity are mostly ineffective in analyzing short sequences that are further corrupted with noise. To address this problem, we propose a new complexity measure ETC and define it as the “Effort To Compress” the input sequence by a lossless compression algorithm. Here, we employ the lossless compression algorithm known as Non-Sequential Recursive Pair Substitution (NSRPS) and define ETC as the number of iterations needed for NSRPS to transform the input sequence to a constant sequence. We demonstrate the utility of ETC in two applications. ETC is shown to have better correlation with Lyapunov exponent than Shannon entropy even with relatively short and noisy time series. The measure also has a greater rate of success in automatic identification and classification of short noisy sequences, compared to entropy and a popular measure based on Lempel-Ziv compression (implemented by Gzip).     

Multiscale Entropy Analysis of Short Signals: The Robustness of Fuzzy Entropy-Based Variants Compared to Full-Length Long Signals

Multiscale entropy (MSE) analysis is a fundamental approach to access the complexity of a time series by estimating its information creation over a range of temporal scales. However, MSE may not be accurate or valid for short time series. This is why previous studies applied different kinds of algorithm derivations to short-term time series. However, no study has systematically analyzed and compared their reliabilities. This study compares the MSE algorithm variations adapted to short time series on both human and rat heart rate variability (HRV) time series using long-term MSE as reference. The most used variations of MSE are studied: composite MSE (CMSE), refined composite MSE (RCMSE), modified MSE (MMSE), and their fuzzy versions. We also analyze the errors in MSE estimations for a range of incorporated fuzzy exponents. The results show that fuzzy MSE versions—as a function of time series length—present minimal errors compared to the non-fuzzy algorithms. The traditional multiscale entropy algorithm with fuzzy counting (MFE) has similar accuracy to alternative algorithms with better computing performance. For the best accuracy, the findings suggest different fuzzy exponents according to the time series length.     

Classification of physiologic and synthetic heart rate variability series using base-scale entropy

The base-scale entropy method was used as a measure to classify physiologic and synthetic heart rate variability series. This method enables analyzing very short, non-stationary, and noisy data. We used it to analyze short-term heart rate variability series. The results show that our method can effectively detect the complex dissimilarity of physiologic time series in different physiologic/pathologic states. We then applied it to the CinC 2002 test datasets. Using the base-scale entropy, we correctly classified 43 of 46 (93%) time series. In combination with time domain analysis, we correctly classified all time series.     

Automatic leukocyte nucleus segmentation by intuitionistic fuzzy divergence based thresholding

The paper proposes a robust approach to automatic segmentation of leukocyte's nucleus from microscopic blood smear images under normal as well as noisy environment by employing a new exponential intuitionistic fuzzy divergence based thresholding technique. The algorithm minimizes the divergence between the actual image and the ideally thresholded image to search for the final threshold. A new divergence formula based on exponential intuitionistic fuzzy entropy has been proposed. Further, to increase its noise handling capacity, a neighborhood-based membership function for the image pixels has been designed. The proposed scheme has been applied on 110 normal and 54 leukemia (chronic myelogenous leukemia) affected blood samples. The nucleus segmentation results have been validated by three expert hematologists. The algorithm achieves an average segmentation accuracy of 98.52% in noise-free environment. It beats the competitor algorithms in terms of several other metrics. The proposed scheme with neighborhood based membership function outperforms the competitor algorithms in terms of segmentation accuracy under noisy environment. It achieves 93.90% and 94.93% accuracies for Speckle and Gaussian noises, respectively. The average area under the ROC curves comes out to be 0.9514 in noisy conditions, which proves the robustness of the proposed algorithm.     

Using the modified sample entropy to detect determinism

A modified sample entropy (mSampEn), based on the nonlinear continuous and convex function, has been proposed and proven to be superior to the standard sample entropy (SampEn) in several aspects. In this Letter, we empirically investigate the ability of the mSampEn statistic combined with surrogate data method to detect determinism. The effects of the datasets length and noise on the proposed method to differentiate between deterministic and stochastic dynamics are tested on several benchmark time series. The noise performance of the mSampEn statistic is also compared with the singular value decomposition (SVD) and symplectic geometry spectrum (SGS) based methods. The results indicate that the mSampEn statistic is a robust index for detecting determinism in short and noisy time series.     

Application of the nonlinear time series prediction method of genetic algorithm for forecasting surface wind of point station in the South China Sea with scatterometer observations

The present work reports the development of nonlinear time series prediction method of genetic algorithm(GA) with singular spectrum analysis(SSA) for forecasting the surface wind of a point station in the South China Sea(SCS) with scatterometer observations.Before the nonlinear technique GA is used for forecasting the time series of surface wind,the SSA is applied to reduce the noise.The surface wind speed and surface wind components from scatterometer observations at three locations in the SCS have been used to develop and test the technique.The predictions have been compared with persistence forecasts in terms of root mean square error.The predicted surface wind with GA and SSA made up to four days(longer for some point station) in advance have been found to be significantly superior to those made by persistence model.This method can serve as a cost-effective alternate prediction technique for forecasting surface wind of a point station in the SCS basin.     

Determining the largest Lyapunov exponent of chaotic dynamics from sequences of interspike intervals contaminated by noise

We discuss abilities of quantifying low-dimensional chaotic oscillations at the input of two threshold models from the output sequences of interspike intervals in the presence of noise. We propose a modification of the standard approach for computing the largest Lyapunov exponent from a time series that verifies the performed estimations for noisy data. We consider features of its application to different types of point processes.     

Permutation Entropy of Weakly Noise-Affected Signals

We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations.     

Maximum entropy analysis of coded images

Maximum entropy reconstruction of coded images which are very noisy or consist of only a small number of detected quanta is considered. It is shown that for data with a high constant variance noise background, maximum entropy allows useful images to be reconstructed from data that is otherwise too noisy. The maximum entropy principle is also applied to quantum limited data where an approach for finding the optimum smoothing is developed which allows information about the location and outline of the object to be deduced from very sparse data. In the neutron imaging example presented, this was done with only 715 detected quanta.     

Distinguishing fingerprints of hyperchaotic and stochastic dynamics in optical chaos from a delayed opto-electronic oscillator

In the dynamics of optical systems, one commonly needs to cope with the problem of coexisting deterministic and stochastic components. The separation of these components is an important, although difficult, task. Often the time scales at which determinism and noise dominate the system's dynamics differ. In this Letter we propose to use information-theory-derived quantifiers, more precisely, permutation entropy and statistical complexity, to distinguish between the two behaviors. Based on experiments of a paradigmatic opto-electronic oscillator, we demonstrate that the time scales at which deterministic or noisy behavior dominate can be identified. Supporting numerical simulations prove the accuracy of this identification.     

Noise reduction for low-dose X-ray CT based on fuzzy logical in stationary wavelet domain

Apparent streak-like artifacts will present in reconstructed images due to excessive quantum noise in low-dose X-ray imaging process. Dealing with the noisy sinogram before a filtered back-projection (FBP) is a useful solution to solve this noise problem. In this paper, we proposed a novel noise restoration method combining wavelet and fuzzy logical technology for low-dose computed tomography (CT) sinogram. The method first utilizes stationary wavelet transform on the noisy sinogram, namely decomposes the sinogram to different resolution levels. And then, at each decomposed resolution level, a fuzzy shrinkage filter is applied to restore the noise-contaminated wavelet coefficients. Simulations were performed and indicated that the proposed method could significantly suppress noise and reduced streak-like artifacts in reconstructed images while at the same time maintaining the image sharpness.     

Efficient noncausal noise reduction for deterministic time series

We present a simple noncausal noise reduction algorithm for time series that consist of noisy measurements of the state vectors of a deterministic (chaotic) nonlinear system. The underlying dynamical system is assumed to be known and to operate in discrete time. The noise reduction algorithm is an iterative scheme for finding exact deterministic orbits close to the measured noisy orbits. Furthermore, we discuss cases where the solution is not the original orbit but homoclinic to it. (c) 2001 American Institute of Physics.     

变分模态分量降噪后重构的水声弱信号检测

针对能量检测法在低信噪比下对非合作水声探测信号的检测性能显著下降的问题,提出了一种组合变分模态分解和小波变换降噪重构的信号检测方法。以信号分解出的各个本征模态函数的近似熵与互相关系数比值作为分量分类参数,将所得分量分为信号分量、含噪信号分量与噪声分量,然后利用第二代小波变换对含噪信号分量降噪后与信号分量组成重构信号,最后对重构信号进行检测。数值仿真结果表明该方法可以在无先验信息的情况下对CW和LFM信号自适应降噪,信噪比0 dB以下时CW信号重构后信噪比提升约12 dB,宽带LFM信号信噪比提升约8～9 dB,有效提升了低虚警概率下信号的检测概率。湖试结果表明,虚警概率为0.1时检测概率可提升至0.9以上,验证了该方法的有效性。     

一种预测混沌时间序列的模糊神经网络方法

给出了一种预测混沌时间序列的模糊神经网络及其学习方法，给出的方法能直接从数据中提取模糊规则，经过优化得到最佳模糊规则库，并利用神经网络的自学习功能修改隶属函数的参数和网络的权值，减少了规则的匹配过程，加快了推理速度，增强了网络的自适应能力. 使用该神经网络及其学习方法对Lorenz混沌时间序列进行了预测仿真研究，试验结果表明给出的预测工具和方法是有效的. 关键词： 模糊神经网络 模糊规则提取 混沌时间序列预测     

基于Bandelets变换的红外图像去噪

提出了一种基于Bandelets变换的红外图像模糊阈值去噪方法,该方法结合了Bandelets变换和模糊阈值在去噪方面的优点.对红外图像进行Bandelets变换的同时,对系数进行模糊阈值处理,实现了图像去噪;同时针对图像去噪问题提出了Bandelets变换中压缩率阈值的选取方法.结果表明,与正交小波硬阈值去噪方法相比,该方法具有良好的去噪性能,并且在去除红外图像噪音的同时,能够获得很好的边缘保持效果.     

Error Covariance Matrix Estimation of Noisy and Dynamically Coupled Time Series

We estimate the covariance matrix of the errors in several dynamically coupled time series corrupted by measurement errors. We say that several scalar time series are dynamically coupled if they record the values of measurements of the state variables of the same smooth dynamical system. The estimation of the covariance matrix of the errors is made using a noise reduction algorithm that efficiently exploits the information contained jointly in the dynamically coupled noisy time series. The method is particularly powerful for short length time series with high uncertainties.