基于双正交小波变换的宫缩信号消噪

小波分析的信号消噪方法是现代信号处理中的重要组成部分,小波基的不同选取将直接影响消噪的效果.本文在全局阈值的标准下,基于不同噪声水平,讨论了小波基的正交性和线性相位性对消噪结果的影响,提出了选取小波基的一般方法,最后利用双正交小波基在软阈值标准下实现了对宫缩信号的消噪处理,并取得了较好的效果.     

When can noise induce chaos and why does it matter: a critique

Noise‐induced chaos illustrates how small amounts of exogenous noise can have disproportionate qualitative impacts on the long term dynamics of a nonlinear system. This property is particularly clear in chaotic systems but is also important for the majority of ecological systems which are nonchaotic, and has direct implications for analyzing ecological time series and testing models against field data. Dennis et al. point out that a definition of chaos which we advocated allows a noise‐dominated system to be classified as chaotic when its Lyapunov exponent λ is positive, which misses what is really going on. As a solution, they propose to eliminate the concept of noise‐induced chaos: chaos “should retain its strictly deterministic definition”, hence “ecological populations cannot be strictly chaotic”. Instead, they suggest that ecologists ask whether ecological systems are strongly influenced by “underlying skeletons with chaotic dynamics or whatever other dynamics”– the skeleton being the hypothetical system that would result if all external and internal noise sources were eliminated. We agree with Dennis et al. about the problem – noise‐dominated systems should not be called chaotic – but not the solution. Even when an estimated skeleton predicts a system's short term dynamics with extremely high accuracy, the skeleton's long term dynamics and attractor may be very different from those of the actual noisy system. Using theoretical models and empirical data on microtine rodent cycles and laboratory populations of Tribolium, we illustrate how data analyses focusing on attributes of the skeleton and its attractor – such as the “deterministic Lyapunov exponent”λ₀ that Dennis et al. have used as their primary indicator of chaos – will frequently give misleading results. In contrast, quantitative measures of the actual noisy system, such as λ, provide useful information for characterizing observed dynamics and for testing proposed mechanistic explanations.     

Analysis of cedar pollen time series: no evidence of low-dimensional chaotic behavior

Much of the current interest in pollen time series analysis is motivated by the possibility that pollen series arise from low-dimensional chaotic systems. If this is the case, short-range prediction using nonlinear modeling is justified and would produce high-quality forecasts that could be useful in providing pollen alerts to allergy sufferers. To date, contradictory reports about the characterization of the dynamics of pollen series can be found in the literature. Pollen series have been alternatively described as featuring and not featuring deterministic chaotic behavior. We showed that the choice of test for detection of deterministic chaos in pollen series is difficult because pollen series exhibit power spectra. This is a characteristic that is also produced by colored noise series, which mimic deterministic chaos in most tests. We proposed to apply the Ikeguchi–Aihara test to properly detect the presence of deterministic chaos in pollen series. We examined the dynamics of cedar (Cryptomeria japonica) hourly pollen series by means of the Ikeguchi–Aihara test and concluded that these pollen series cannot be described as low-dimensional deterministic chaos. Therefore, the application of low-dimensional chaotic deterministic models to the prediction of short-range pollen concentration will not result in high-accuracy pollen forecasts even though these models may provide useful forecasts for certain applications. We believe that our conclusion can be generalized to pollen series from other wind-pollinated plant species, as wind speed, the forcing parameter of the pollen emission and transport, is best described as a nondeterministic series that originates in the high dimensionality of the atmosphere.     

Non-invasive diagnosis methods of coronary disease based on wavelet denoising and sound analyzing

The heart sound is the characteristic signal of cardiovascular health status. The objective of this project is to explore the correlation between Wavelet Transform and noise performance of heart sound and the adaptability of classifying heart sound using bispectrum estimation. Since the wavelet has multi-scale and multi-resolution characteristics, in this paper, the heart sound signal with different frequency ranges is decomposed through wavelet and displayed on different scales of the resolving wavelet result. According to distribution features of frequency of heart sound signals, the interference components in heart sound signal can be eliminated by selecting reconstruction coefficients. Comparing de-noising effects of four wavelets which are haar, db6, sym8 and coif6, the db6 wavelet has achieved an optimal denoising effect to heart sound signals. The de-noising result of contrasting different layers in the db6 wavelet shows that decomposing with five layers in db6 provide the optimal performance. In practice, the db6 wavelet also shows commendable denoising effects when applying to 51 clinical heart signals. Furthermore, through the clinic analyses of 29 normal signals from healthy people and 22 abnormal heart signals from coronary heart disease patients, this method can fairly distinguish abnormal signals from normal signals by applying bispectrum estimation to denoised signals via ARMA coefficients model.     

基因表达数据小波降噪与肿瘤识别

建立了基于小波降噪和支持向量机的结肠癌基因表达数据肿瘤识别模型.对试验数据进行小波分解,并利用交叉验证的方法计算试验样本的平均分类准确率,确定小波函数与小波分解层数;引入能量阈值方法对小波分解系数进行阈值处理,达到降噪的目的;提出了基因分类贡献率与主成分分析结合的方法,提取结肠癌样本数据特征;利用支持向量机强大的非线性映射能力,实现对结肠癌样本数据的非线性分类.为了减弱样本集的划分对分类准确率的影响,本文采取Jackknife检验方法对支持向量分类器的分类器检验,其分类准确率为96.77%.试验结果证明了该方法的有效性,该方法对结肠癌的识别具有一定的参考价值.     

Denoising Single-Molecule FRET Trajectories with Wavelets and Bayesian Inference

A method to denoise single-molecule fluorescence resonance energy (smFRET) trajectories using wavelet detail thresholding and Bayesian inference is presented. Bayesian methods are developed to identify fluorophore photoblinks in the time trajectories. Simulated data are used to quantify the improvement in static and dynamic data analysis. Application of the method to experimental smFRET data shows that it distinguishes photoblinks from large shifts in smFRET efficiency while maintaining the important advantage of an unbiased approach. Known sources of experimental noise are examined and quantified as a means to remove their contributions via soft thresholding of wavelet coefficients. A wavelet decomposition algorithm is described, and thresholds are produced through the knowledge of noise parameters in the discrete-time photon signals. Reconstruction of the signals from thresholded coefficients produces signals that contain noise arising only from unquantifiable parameters. The method is applied to simulated and observed smFRET data, and it is found that the denoised data retain their underlying dynamic properties, but with increased resolution.     

Energy Detection Based on Undecimated Discrete Wavelet Transform and Its Application in Magnetic Anomaly Detection

Magnetic anomaly detection (MAD) is a passive approach for detection of a ferromagnetic target, and its performance is often limited by external noises. In consideration of one major noise source is the fractal noise (or called 1/f noise) with a power spectral density of 1/f^a (0<a<2), which is non-stationary, self-similarity and long-range correlation. Meanwhile the orthonormal wavelet decomposition can play the role of a Karhunen-Loève-type expansion to the 1/f-type signal by its decorrelation abilities, an effective energy detection method based on undecimated discrete wavelet transform (UDWT) is proposed in this paper. Firstly, the foundations of magnetic anomaly detection and UDWT are introduced in brief, while a possible detection system based on giant magneto-impedance (GMI) magnetic sensor is also given out. Then our proposed energy detection based on UDWT is described in detail, and the probabilities of false alarm and detection for given the detection threshold in theory are presented. It is noticeable that no a priori assumptions regarding the ferromagnetic target or the magnetic noise probability are necessary for our method, and different from the discrete wavelet transform (DWT), the UDWT is shift invariant. Finally, some simulations are performed and the results show that the detection performance of our proposed detector is better than that of the conventional energy detector even utilized in the Gaussian white noise, especially when the spectral parameter α is less than 1.0. In addition, a real-world experiment was done to demonstrate the advantages of the proposed method.     

Robust permanence and impermanence for stochastic replicator dynamics

Garay and Hofbauer (SIAM J. Math. Anal. 34 (2003)) proposed sufficient conditions for robust permanence and impermanence of the deterministic replicator dynamics. We reconsider these conditions in the context of the stochastic replicator dynamics, which is obtained from its deterministic analogue by introducing Brownian perturbations of payoffs. When the deterministic replicator dynamics is permanent and the noise level small, the stochastic dynamics admits a unique ergodic distribution whose mass is concentrated near the maximal interior attractor of the unperturbed system; thus, permanence is robust against small unbounded stochastic perturbations. When the deterministic dynamics is impermanent and the noise level small or large, the stochastic dynamics converges to the boundary of the state space at an exponential rate.     

Bayesian Analysis for Uncertainty and Risk in a Groundwater Numerical Model's Predictions

Groundwater modeling typically relies on some hypothesis and approximations of reality, as the real hydrologic systems are far more complex than we can mathematically characterize. This kind of a model's errors cannot be neglected in the uncertainty analysis for a model's predictions in practical issues. As the scale and complexity increase, the associated uncertainties boost dramatically. In this study, a Bayesian uncertainty analysis method for a deterministic model's predictions is presented. The geostatistics of hydrogeologic parameters obtained from site characterization are treated as the prior parameter distribution in the Bayes’ theorem. Then the Markov-Chain Monte Carlo method is used to generate the posterior statistical distribution of the model's predictions, conditional to the observed hydrologic system behaviors. Finally, a series of synthetic examples are given by applying this method to a MODFLOW pumping test model, to test its capability and efficiency in order to assess various sources of the model's prediction uncertainty. The impacts of the model's parameter sensitivity, simplification, and observation errors to predict uncertainty are evaluated, respectively. The results are analyzed statistically to provide deterministic predictions with associated prediction errors. Risk analysis is also derived from the Bayesian results to draw tradeoff curves for decision-making about exploitation of groundwater resources.     

Denoising of ECG signals based on noise reduction algorithms in EMD and wavelet domains

This paper presents a new ECG denoising approach based on noise reduction algorithms in empirical mode decomposition (EMD) and discrete wavelet transform (DWT) domains. Unlike the conventional EMD based ECG denoising approaches that neglect a number of initial intrinsic mode functions (IMFs) containing the QRS complex as well as noise, we propose to perform windowing in the EMD domain in order to reduce the noise from the initial IMFs instead of discarding them completely thus preserving the QRS complex and yielding a relatively cleaner ECG signal. The signal thus obtained is transformed in the DWT domain, where an adaptive soft thresholding based noise reduction algorithm is employed considering the advantageous properties of the DWT compared to that of the EMD in preserving the energy in the presence of noise and in reconstructing the original ECG signal with a better time resolution. Extensive simulations are carried out using the MIT-BIH arrythmia database and the performance of the proposed method is evaluated in terms of several standard metrics. The simulation results show that the proposed method is able to reduce noise from the noisy ECG signals more accurately and consistently in comparison to some of the stateof-the-art methods.     

Classification of epileptic seizures using wavelet packet log energy and norm entropies with recurrent Elman neural network classifier

Electroencephalogram shortly termed as EEG is considered as the fundamental segment for the assessment of the neural activities in the brain. In cognitive neuroscience domain, EEG-based assessment method is found to be superior due to its non-invasive ability to detect deep brain structure while exhibiting superior spatial resolutions. Especially for studying the neurodynamic behavior of epileptic seizures, EEG recordings reflect the neuronal activity of the brain and thus provide required clinical diagnostic information for the neurologist. This specific proposed study makes use of wavelet packet based log and norm entropies with a recurrent Elman neural network (REN) for the automated detection of epileptic seizures. Three conditions, normal, pre-ictal and epileptic EEG recordings were considered for the proposed study. An adaptive Weiner filter was initially applied to remove the power line noise of 50 Hz from raw EEG recordings. Raw EEGs were segmented into 1 s patterns to ensure stationarity of the signal. Then wavelet packet using Haar wavelet with a five level decomposition was introduced and two entropies, log and norm were estimated and were applied to REN classifier to perform binary classification. The non-linear Wilcoxon statistical test was applied to observe the variation in the features under these conditions. The effect of log energy entropy (without wavelets) was also studied. It was found from the simulation results that the wavelet packet log entropy with REN classifier yielded a classification accuracy of 99.70 % for normal-pre-ictal, 99.70 % for normal-epileptic and 99.85 % for pre-ictal-epileptic.     

Automated Protein NMR Structure Determination Using Wavelet De-noised NOESY Spectra

A major time-consuming step of protein NMR structure determination is the generation of reliable NOESY cross peak lists which usually requires a significant amount of manual interaction. Here we present a new algorithm for automated peak picking involving wavelet de-noised NOESY spectra in a process where the identification of peaks is coupled to automated structure determination. The core of this method is the generation of incremental peak lists by applying different wavelet de-noising procedures which yield peak lists of a different noise content. In combination with additional filters which probe the consistency of the peak lists, good convergence of the NOESY-based automated structure determination could be achieved. These algorithms were implemented in the context of the ARIA software for automated NOE assignment and structure determination and were validated for a polysulfide-sulfur transferase protein of known structure. The procedures presented here should be commonly applicable for efficient protein NMR structure determination and automated NMR peak picking. Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.     

带噪生物实验数据的不确定支持向量数据描述

在对候选基因进行排序时,支持向量数据描述（SVDD）可以用来描述各种异构的数据源,如序列数据、学术文献数据、各种生物实验数据等。由于生物实验数据带有噪声,在用SVDD对其描述时,会遇到噪声的影响。本研究通过公式推导扩展了原始的SVDD,提出不确定支持向量数据描述（USVDD）,用来降低噪声的影响。利用酵母基因表达数据进行实验,结果表明该方法比标准的SVDD对带噪声的数据具有更好的描述能力。     

Removal of ECG interference from surface respiratory electromyography

The signal to noise ratio (SNR) of surface respiratory electromyography signal is very low. Indeed EMG signal is contaminated by different types of noise especially the cardiac artefact ECG. This article explores the problem of removing ECG artefact from respiratory EMG signal. The new method uses an adaptive structure with an electrocardyographic ECG reference signal carried out by wavelet decomposition. The proposed algorithm requires only one channel to both estimating the adaptive filter input reference noise and the respiratory EMG signal. This new technique demonstrates how two steps will be combined: the first step decomposes the signal with forward discrete wavelet transform into sub-bands to get the wavelet coefficients. Then, an improved soft thresholding function was applied. And the ECG input reference signal is reconstructed with the transformed coefficients whereas, the second uses an adaptive filter especially the LMS one to remove the ECG signal. After trying statistical as well as mathematical analysis, the complete investigation ensures that all details and steps make proof that our rigorous method is appropriate. Compared to the results obtained using previous techniques, the results achieved using the new algorithm show a significant improvement in the efficiency of the ECG rejection.     

Simple and Robust Realtime QRS Detection Algorithm Based on Spatiotemporal Characteristic of the QRS Complex

The purpose of this research is to develop an intuitive and robust realtime QRS detection algorithm based on the physiological characteristics of the electrocardiogram waveform. The proposed algorithm finds the QRS complex based on the dual criteria of the amplitude and duration of QRS complex. It consists of simple operations, such as a finite impulse response filter, differentiation or thresholding without complex and computational operations like a wavelet transformation. The QRS detection performance is evaluated by using both an MIT-BIH arrhythmia database and an AHA ECG database (a total of 435,700 beats). The sensitivity (SE) and positive predictivity value (PPV) were 99.85% and 99.86%, respectively. According to the database, the SE and PPV were 99.90% and 99.91% in the MIT-BIH database and 99.84% and 99.84% in the AHA database, respectively. The result of the noisy environment test using record 119 from the MIT-BIH database indicated that the proposed method was scarcely affected by noise above 5 dB SNR (SE = 100%, PPV > 98%) without the need for an additional de-noising or back searching process.     

Improving surface EMG burst detection in infrahyoid muscles during swallowing using digital filters and discrete wavelet analysis

The visual inspection is a widely used method for evaluating the surface electromyographic signal (sEMG) during deglutition, a process highly dependent of the examiners expertise. It is desirable to have a less subjective and automated technique to improve the onset detection in swallowing related muscles, which have a low signal-to-noise ratio. In this work, we acquired sEMG measured in infrahyoid muscles with high baseline noise of ten healthy adults during water swallowing tasks. Two methods were applied to find the combination of cutoff frequencies that achieve the most accurate onset detection: discrete wavelet decomposition based method and fixed steps variations of low and high cutoff frequencies of a digital bandpass filter. Teager-Kaiser Energy operator, root mean square and simple threshold method were applied for both techniques. Results show a narrowing of the effective bandwidth vs. the literature recommended parameters for sEMG acquisition. Both level 3 decomposition with mother wavelet db4 and bandpass filter with cutoff frequencies between 130 and 180 Hz were optimal for onset detection in infrahyoid muscles. The proposed methodologies recognized the onset time with predictive power above 0.95, that is similar to previous findings but in larger and more superficial muscles in limbs.     

小波和主分量分析方法研究思维脑电

研究自发脑电和思维活动的关系．利用小波和主分量分析结合的WPCA算法对不同思维任务记录的六导脑电进行处理,并对思维特征的频谱能量和变化率等多指标进行综合分析和计算。结果表明WPCA算法不仅可以实现噪声的去除,而且能提高主分量的贡献率,降低输入矢量的维数。对脑电主分量的分析揭示了脑电与思维个体、思维种类、复杂度以及注意力的联系,思维任务的神经网络分类结果验证了WPCA方法研究脑电和思维的有效性,为进一步理解认知和思维过程,实现对思维的定位和分类提供了依据。     

Detecting determinism in short time series, with an application to the analysis of a stationary EEG recording

We have developed a new method for detecting determinism in a short time series and used this method to examine whether a stationary EEG is deterministic or stochastic. The method is based on the observation that the trajectory of a time series generated from a differentiable dynamical system behaves smoothly in an embedded phase space. The angles between two successive directional vectors in the trajectory reconstructed from a time series at a minimum embedding dimension were calculated as a function of time. We measured the irregularity of the angle variations obtained from the time series using second-order difference plots and central tendency measures, and compared these values with those from surrogate data. The ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated time series, including data from Lorenz, R?ssler, and Van der Pol attractors, high-dimensional equations, and 1/f noise. We then applied this method to the analysis of stationary segments of EEG recordings consisting of 750 data points (6-s segments) from five normal subjects. The stationary EEG segments were not found to exhibit deterministic components. This method can be used to analyze determinism in short time series, such as those from physiological recordings, that can be modeled using differentiable dynamical processes.     

Unraveling past impacts of climate change and land management on historic peatland development using proxy‐based reconstruction,monitoring data and process modeling

Peatlands represent globally significant soil carbon stores that have been accumulating for millennia under water‐logged conditions. However, deepening water‐table depths (WTD) from climate change or human‐induced drainage could stimulate decomposition resulting in peatlands turning from carbon sinks to carbon sources. Contemporary WTD ranges of testate amoebae (TA) are commonly used to predict past WTD in peatlands using quantitative transfer function models. Here we present, for the first time, a study comparing TA‐based WTD reconstructions to instrumentally monitored WTD and hydrological model predictions using the MILLENNIA peatland model to examine past peatland responses to climate change and land management. Although there was very good agreement between monitored and modeled WTD, TA‐reconstructed water table was consistently deeper. Predictions from a larger European TA transfer function data set were wetter, but the overall directional fit to observed WTD was better for a TA transfer function based on data from northern England. We applied a regression‐based offset correction to the reconstructed WTD for the validation period (1931–2010). We then predicted WTD using available climate records as MILLENNIA model input and compared the offset‐corrected TA reconstruction to MILLENNIA WTD predictions over an extended period (1750–1931) with available climate reconstructions. Although the comparison revealed striking similarities in predicted overall WTD patterns, particularly for a recent drier period (1965–1995), there were clear periods when TA‐based WTD predictions underestimated (i.e. drier during 1830–1930) and overestimated (i.e. wetter during 1760–1830) past WTD compared to MILLENNIA model predictions. Importantly, simulated grouse moor management scenarios may explain the drier TA WTD predictions, resulting in considerable model predicted carbon losses and reduced methane emissions, mainly due to drainage. This study demonstrates the value of a site‐specific and combined data‐model validation step toward using TA‐derived moisture conditions to understand past climate‐driven peatland development and carbon budgets alongside modeling likely management impacts.     

Stochastic analogues of deterministic single-species population models

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models--additive normally distributed noise and multiplicative lognormally distributed noise--generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.