小波分析在生态环境研究中的应用初探

小波分析(Wavelet Analysis)是时间-频率分析领域近年来迅速发展的一种新技术,具有多时间尺度,多层次和多分辨的特性,已被广泛地应用在信号分析、信息分析和地球科学研究上.本文以大亚湾大鹏澳水域2002年春秋两季浮游植物30d连续观测资料为例,首次运用小波技术分析浮游植物对生境变化的响应特征.结果表明,通过小波变换的浮游植物数量(细胞密度)的时间序列,存在各自的优势周期和多时间尺度结构特征,而春秋两季浮游植物细胞密度的优势周期和多时间尺度结构,在大尺度上大致相同,但在小尺度结构上稍有差别;使用不同小波变换(如Mexh小波变换和Morlet小波变换)可以取得各自不同特点的结果.本文对小波分析技术在生态环境研究的初步应用说明,小波分析技术可以对生态系统中浮游植物的动态变化进行多时间尺度,多层次和多分辨的分析,为深入研究和预测浮游植物的动态变化提供一种新的分析手段.     

A new algorithm for wavelet-based heart rate variability analysis

One of the most promising non-invasive markers of the activity of the autonomic nervous system is heart rate variability (HRV). HRV analysis toolkits often provide spectral analysis techniques using the Fourier transform, which assumes that the heart rate series is stationary. To overcome this issue, the Short Time Fourier Transform (STFT) is often used. However, the wavelet transform is thought to be a more suitable tool for analyzing non-stationary signals than the STFT. Given the lack of support for wavelet-based analysis in HRV toolkits, such analysis must be implemented by the researcher. This has made this technique underutilized.This paper presents a new algorithm to perform HRV power spectrum analysis based on the Maximal Overlap Discrete Wavelet Packet Transform (MODWPT). The algorithm calculates the power in any spectral band with a given tolerance for the band's boundaries. The MODWPT decomposition tree is pruned to avoid calculating unnecessary wavelet coefficients, thereby optimizing execution time. The center of energy shift correction is applied to achieve optimum alignment of the wavelet coefficients. This algorithm has been implemented in RHRV, an open-source package for HRV analysis. To the best of our knowledge, RHRV is the first HRV toolkit with support for wavelet-based spectral analysis.     

The use of the Mexican Hat and the Morlet wavelets for detection of ecological patterns

In this paper, we compare the relationship between scale and period in ecological pattern analysis and wavelet analysis. We also adapt a commonly used wavelet, the Morlet, to ecological pattern analysis. Using Monte Carlo assessments, we apply methods of statistical significance test to wavelet analysis for pattern analysis. In order to understand the inherent strength and weakness of the Morlet and the Mexican Hat wavelets, we also investigate and compare the properties of two frequently used wavelets by testing with field data and four artificial transects of different typical patterns which is often encountered in ecological research. It is shown that the Mexican Hat provides better detection and localization of patch and gap events over the Morlet, whereas the Morlet offers improved detection and localization of scale over the Mexican Hat. There is always a trade-off between the detection and localization of scale versus patch and gap events. Therefore, the best composite analysis is the combination of their advantages. The properties of wavelet in dealing with ecological data may be affected by characteristics intrinsic to wavelet itself. The peaks of different scales in isograms of wavelet power spectrum from the Mexican Hat may overlap with each other. Alternatively, these peaks of different scales in isograms of wavelet power spectrum may combine with each other unless the size of the analyzed scales is significantly different. These overlapping or combining lead to combining of peaks for different scales, or the masking of trough between peaks of different scales in the scalogram. Ecologists should combine all the information in scalogram and isograms of wavelet coefficient and wavelet power spectrum from different wavelets, which can provide us a broader view and precise pattern information.     

Answering six questions in extracting children��s mismatch negativity through combining wavelet decomposition and independent component analysis

This study combines wavelet decomposition and independent component analysis (ICA) to extract mismatch negativity (MMN) from electroencephalography (EEG) recordings. As MMN is a small event-related potential (ERP), a systematic ICA based approach is designed, exploiting MMN’s temporal, frequency and spatial information. Moreover, this study answers which type of EEG recordings is more appropriate for ICA to extract MMN, what kind of the preprocessing is beneficial for ICA decomposition, which algorithm of ICA can be chosen to decompose EEG recordings under the selected type, how to determine the desired independent component extracted by ICA, how to improve the accuracy of the back projection of the selected independent component in the electrode field, and what can be finally obtained with the application of ICA. Results showed that the proposed method extracted MMN with better properties than those estimated by difference wave only using temporal information or ICA only using spatial information. The better properties mean that the deviant with larger magnitude of deviance to repeated stimuli in the oddball paradigm can elicit MMN with larger peak amplitude and shorter latency. As other ERPs also have the similar information exploited here, the proposed method can be used to study other ERPs.     

Discrete wavelet transform: a tool in smoothing kinematic data

Motion analysis systems typically introduce noise to the displacement data recorded. Butterworth digital filters have been used to smooth the displacement data in order to obtain smoothed velocities and accelerations. However, this technique does not yield satisfactory results, especially when dealing with complex kinematic motions that occupy the low- and high-frequency bands. The use of the discrete wavelet transform, as an alternative to digital filters, is presented in this paper. The transform passes the original signal through two complementary low- and high-pass FIR filters and decomposes the signal into an approximation function and a detail function. Further decomposition of the signal results in transforming the signal into a hierarchy set of orthogonal approximation and detail functions. A reverse process is employed to perfectly reconstruct the signal (inverse transform) back from its approximation and detail functions. The discrete wavelet transform was applied to the displacement data recorded by Pezzack et al., 1977. The smoothed displacement data were twice differentiated and compared to Pezzack et al.'s acceleration data in order to choose the most appropriate filter coefficients and decomposition level on the basis of maximizing the percentage of retained energy (PRE) and minimizing the root mean square error (RMSE). Daubechies wavelet of the fourth order (Db4) at the second decomposition level showed better results than both the biorthogonal and Coiflet wavelets (PRE = 97.5%, RMSE = 4.7 rad s-2). The Db4 wavelet was then used to compress complex displacement data obtained from a noisy mathematically generated function. Results clearly indicate superiority of this new smoothing approach over traditional filters.     

小波相干分析及其在听觉与震动刺激事件相关电位处理中的应用

尝试将小波相干方法应用于事件相关电位实验的脑电信号分析中。实验分为三组：听觉任务、震动任务1和震动任务2。对12个受试者的实验数据进行40Hz左右的小波相干分析,计算了前额脑区与其他各脑区之间的相干性,发现震动任务的小波相干值大于听觉任务并有显著差异,且在不同的任务中,各脑区的小波相干值有其明显不同的分布特征,且随时间呈有规律的变化。分析体现了小波相干在短时脑电信号处理上的优势。     

Wavelet analysis for detecting anisotropy in point patterns

Although many methods have been proposed for analysing point locations for spatial pattern, previous methods have concentrated on clumping and spacing. The study of anisotropy (changes in spatial pattern with direction) in point patterns has been limited by lack of methods explicitly designed for these data and this purpose; researchers have been constrained to choosing arbitrary test directions or converting their data into quadrat counts and using methods designed for continuously distributed data. Wavelet analysis, a booming approach to studying spatial pattern, widely used in mathematics and physics for signal analysis, has started to make its way into the ecological literature. A simple adaptation of wavelet analysis is proposed for the detection of anisotropy in point patterns. The method is illustrated with both simulated and field data. This approach can easily be used for both global and local spatial analysis.     

基于小波和BP网络的视觉诱发电位分类识别

提出了小波分解与BP网络相结合的方法来识别视觉诱发电位（Visual Evoked Potential,VEP）。先用小波分解对VEP进行特征提取和降维。然后用BP网络进行分类识别。     

飞行状态下四种菊头蝠回声定位声波的小波包识别方法

研究了飞行状态下的四种菊头蝠回声定位声波的识别方法.通过小波包分解得到各个频带能量作为识一别特征向量,用主成分分析法优化特征空间.提取少数几个主成分,这些主成分彼此不相关,符合特征优化的要求,以主成分向量作为BP神经网络的输入对蝙蝠的种类进行识别.个体识别正确率达到了80%以上,表明基于小渡包分解和神经网络识别的方法对蝙蝠回声定位声波进行识别是可行的.     

一个新的脑电信号分析系统：小波分析理论的运用

小波变换是一种把时间、频率（或尺度）两域结合起来的分析方法。它被誉为“分析信号的数学显微镜”。本系统将小波变换用于脑电信号分析,是一个在Ｗｉｎｄｏｗｓ３．１下开发的脑电分析系统。     

南京市城市景观的特征尺度

在RS技术支持下,采用分辨率为10m的SPOT-5遥感影像为数据源,分别应用Haar、Morlet、Mexican Hat 3种基小波,对南京市江北城郊、主城区和东南城郊3种不同景观类型进行了特征尺度研究。结果表明,Modet基小波最适于进行城市景观的特征尺度检测,Mexican Hat基小波对粒级嵌套结构检测效果稍差,而Haar基小波不适于对连续型数据源的景观进行特征尺度检测。Morlet基小波的一维小波分析结果表明,南京市江北城郊和东南城郊都存在1个对应于各自农田斑块平均粒径的特征尺度,分别为362m和446m,而主城区则检测出存在3个特征尺度,即：292、835m和2200m,分别对应于建筑小区、小型街区和大型街区的平均粒径,显示主城区存在具有等级结构特征的“建筑小区-小型街区-大型街区”的粒级嵌套结构,揭示了城区具有比城郊复杂得多的粒级结构特征。     

A comparison among different techniques for human ERG signals processing and classification

Feature detection in biomedical signals is crucial for deepening our knowledge about the involved physiological processes. To achieve this aim, many analytic approaches can be applied but only few are able to deal with signals whose time dependent features provide useful clinical information. Among the biomedical signals, the electroretinogram (ERG), that records the retinal response to a light flash, can improve our comprehension of the complex photoreceptoral activities.The present study is focused on the analysis of the early response of the photoreceptoral human system, known as a-wave ERG-component. This wave reflects the functional integrity of the photoreceptors, rods and cones, whose activation dynamics are not yet completely understood. Moreover, since in incipient photoreceptoral pathologies eventual anomalies in a-wave are not always detectable with a “naked eye” analysis of the traces, the possibility to discriminate pathologic from healthy traces, by means of appropriate analytical techniques, could help in clinical diagnosis.In the present paper, we discuss and compare the efficiency of various techniques of signal processing, such as Fourier analysis (FA), Principal Component Analysis (PCA), Wavelet Analysis (WA) in recognising pathological traces from the healthy ones. The investigated retinal pathologies are Achromatopsia, a cone disease and Congenital Stationary Night Blindness, affecting the photoreceptoral signal transmission. Our findings prove that both PCA and FA of conventional ERGs, don't add clinical information useful for the diagnosis of ocular pathologies, whereas the use of a more sophisticated analysis, based on the wavelet transform, provides a powerful tool for routine clinical examinations of patients.     

Using support vector machines to distinguish enzymes: Approached by incorporating wavelet transform

The enzymatic attributes of newly found protein sequences are usually determined either by biochemical analysis of eukaryotic and prokaryotic genomes or by microarray chips. These experimental methods are both time-consuming and costly. With the explosion of protein sequences registered in the databanks, it is highly desirable to develop an automated method to identify whether a given new sequence belongs to enzyme or non-enzyme. The discrete wavelet transform (DWT) and support vector machine (SVM) have been used in this study for distinguishing enzyme structures from non-enzymes. The networks have been trained and tested on two datasets of proteins with different wavelet basis functions, decomposition scales and hydrophobicity data types. Maximum accuracy has been obtained using SVM with a wavelet function of Bior2.4, a decomposition scale j=5, and Kyte-Doolittle hydrophobicity scales. The results obtained by the self-consistency test, jackknife test and independent dataset test are encouraging, which indicates that the proposed method can be employed as a useful assistant technique for distinguishing enzymes from non-enzymes.     

脑电信号数据压缩及棘波识别的小波神经网络方法

本文在对小波神经网络及其算法研究的基础上,提出了一种对脑电信号压缩表达和痫样脑电棘波识别的新方法。实验结果显示,小波网络在大量压缩数据的同时,能够较好的恢复原有信号,另外,在脑电信号的时频谱等高线图上,得到了易于自动识别的棘波和棘慢复合波特征,说明此方法在电生理信号处理和时频分析方面有着光明的应用前景。     

Modeling activity patterns of wildlife using time‐series analysis

The study of wildlife activity patterns is an effective approach to understanding fundamental ecological and evolutionary processes. However, traditional statistical approaches used to conduct quantitative analysis have thus far had limited success in revealing underlying mechanisms driving activity patterns. Here, we combine wavelet analysis, a type of frequency‐based time‐series analysis, with high‐resolution activity data from accelerometers embedded in GPS collars to explore the effects of internal states (e.g., pregnancy) and external factors (e.g., seasonal dynamics of resources and weather) on activity patterns of the endangered giant panda (Ailuropoda melanoleuca). Giant pandas exhibited higher frequency cycles during the winter when resources (e.g., water and forage) were relatively poor, as well as during spring, which includes the giant panda's mating season. During the summer and autumn when resources were abundant, pandas exhibited a regular activity pattern with activity peaks every 24 hr. A pregnant individual showed distinct differences in her activity pattern from other giant pandas for several months following parturition. These results indicate that animals adjust activity cycles to adapt to seasonal variation of the resources and unique physiological periods. Wavelet coherency analysis also verified the synchronization of giant panda activity level with air temperature and solar radiation at the 24‐hr band. Our study also shows that wavelet analysis is an effective tool for analyzing high‐resolution activity pattern data and its relationship to internal and external states, an approach that has the potential to inform wildlife conservation and management across species.     

Energy-Based Wavelet De-Noising of Hydrologic Time Series

De-noising is a substantial issue in hydrologic time series analysis, but it is a difficult task due to the defect of methods. In this paper an energy-based wavelet de-noising method was proposed. It is to remove noise by comparing energy distribution of series with the background energy distribution, which is established from Monte-Carlo test. Differing from wavelet threshold de-noising (WTD) method with the basis of wavelet coefficient thresholding, the proposed method is based on energy distribution of series. It can distinguish noise from deterministic components in series, and uncertainty of de-noising result can be quantitatively estimated using proper confidence interval, but WTD method cannot do this. Analysis of both synthetic and observed series verified the comparable power of the proposed method and WTD, but de-noising process by the former is more easily operable. The results also indicate the influences of three key factors (wavelet choice, decomposition level choice and noise content) on wavelet de-noising. Wavelet should be carefully chosen when using the proposed method. The suitable decomposition level for wavelet de-noising should correspond to series'' deterministic sub-signal which has the smallest temporal scale. If too much noise is included in a series, accurate de-noising result cannot be obtained by the proposed method or WTD, but the series would show pure random but not autocorrelation characters, so de-noising is no longer needed.     

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.     

小波变换及其在医学图像处理中的应用

医学图像的好坏直接影响着医生对病情的诊断和治疗,因此利用数字图像处理等技术对医学图像进行有效的处理,已成为医学图像处理研究和开发的一大热点。小波变换是对傅里叶变换的继承和发展,在医学影像领域有着广泛的应用前景。本文介绍了二维离散小渡变换的一般形式,在图像分解与重构的基础上．系统地阐述了利用小小组变换的时频域特性与多分辨分析对医学图像进行去噪、增强以及边缘提取等深层次的处理,有效的改善图像质量。     

基于多尺度植物种子图像边缘检测算法的设计与实现

小波变换,由于其具有时频局部化的特性及多尺度特性,能敏感地反映突变信号,是一种理想的边缘提取方法．本文系统地介绍了作者在图像边缘检测方面所做的理论探讨、算法及应用研究工作．目前的边缘提取方法有多种,本文将重点集中于基于小波变换的图像边缘检测方法的理论推导和算法实现．     

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.