Despeckling of medical ultrasound images using Daubechies complex wavelet transform

The paper presents a novel despeckling method, based on Daubechies complex wavelet transform, for medical ultrasound images. Daubechies complex wavelet transform is used due to its approximate shift invariance property and extra information in imaginary plane of complex wavelet domain when compared to real wavelet domain. A wavelet shrinkage factor has been derived to estimate the noise-free wavelet coefficients. The proposed method firstly detects strong edges using imaginary component of complex scaling coefficients and then applies shrinkage on magnitude of complex wavelet coefficients in the wavelet domain at non-edge points. The proposed shrinkage depends on the statistical parameters of complex wavelet coefficients of noisy image which makes it adaptive in nature. Effectiveness of the proposed method is compared on the basis of signal to mean square error (SMSE) and signal to noise ratio (SNR). The experimental results demonstrate that the proposed method outperforms other conventional despeckling methods as well as wavelet based log transformed and non-log transformed methods on test images. Application of the proposed method on real diagnostic ultrasound images has shown a clear improvement over other methods.     

一维小波变换在时域光学相干层析成像中的应用

时域光学相干层析(OCT)系统通常采用短时傅里叶变换(STFT)完成干涉信号的解调和图像重构。短时傅里叶变换算法简单,但是在干涉信号解调时难以获得好的去噪效果,通常还需在二维(2D)图像域对重构图像进行去噪。该方法数据运算量大,集成度不高。将一维(1D)小波变换(WT)应用于时域光学相干层析成像技术,同时实现干涉信号解调、去噪和图像重构。算法将时域光学相干层析的干涉信号分解到各个不同的频率空间,保留包含调制频率的频率空间的小波系数,对保留的小波系数进行滤波去噪后进行逆变换即可实现对干涉信号的解调和去噪,对解调信号等间距采样实现图像重构。该方法数据运算量小,集成度高,结合先进的小波去噪技术可以大大提高重构图像的分辨率,具有良好的应用前景。     

Analysis of EMG signals by means of the matched wavelet transform

The authors apply the wavelet transform to the analysis of EMG signals. Exploiting the fact that, under certain conditions, the signal can be considered as the sum of scaled and delayed versions of a single prototype, we have chosen the mother wavelet so as to match the known shape of the basic component. Moreover, the input signal has been Shannon interpolated in order to improve the low scale resolution. The results in terms of MUAP detection and resolution are very encouraging, even in the presence of high levels of noise     

在线脑机接口中脑电信号的特征提取与分类方法

在脑机接口研究中,针对运动想象脑电信号的特征抽取,提出了一种基于离散小波变换和AR模型的方法.利用Daubechies类小波函数对脑电信号进行3层分解,抽取小波变换系数的统计特征;利用Burg算法提取脑电信号6阶AR模型系数.将这两类特征进行组合后使用神经网络、支持向量机、马氏距离线性判别进行分类并比较分析.采用BCI...     

一种高性能对称FIR系数的推导及其应用

Daubechies 小波双尺度方程系数(可看作FIR滤波器)在数字信号处理领域得到了广泛的应用，这说明了小波双尺度方程系数比小波函数本身更有吸引力。本文作者试图通过经典的付氏分析理论，应用与Daubechies 不同的方法，从不同的角度，推导出一种新的对称小波双尺度方程系数(可看作对称FIR滤波器)，力图浅显易懂，严格合理。     

A model for the generation of synthetic intramuscular EMG signals to test decomposition algorithms

As more and more intramuscular electromyogram (EMG) decomposition programs are being developed, there is a growing need for evaluating and comparing their performances. One way to achieve this goal is to generate synthetic EMG signals having known features. Features of interest are: the number of channels acquired (number of detection surfaces), the number of detected motor unit action potential (MUAP) trains, their time-varying firing rates, the degree of shape similarity among MUAPs belonging to the same motor unit (MU) or to different MUs, the degree of MUAP superposition, the MU activation intervals, the amount and type of additive noise. A model is proposed to generate one or more channels of intramuscular EMG starting from a library of real MUAPs represented in a 16-dimensional space using their Associated Hermite expansion. The MUAP shapes, regularity of repetition rate, degree of superposition, activation intervals, etc. may be time variable and are described quantitatively by a number of parameters which define a stochastic process (the model) with known statistical features. The desired amount of noise may be added to the synthetic signal which may then be processed by the decomposition algorithm under test to evaluate its capability of recovering the signal features.     

Compression of biomedical signals with mother wavelet optimization and best-basis wavelet packet selection

We propose a novel scheme for signal compression based on the discrete wavelet packet transform (DWPT) decompositon. The mother wavelet and the basis of wavelet packets were optimized and the wavelet coefficients were encoded with a modified version of the embedded zerotree algorithm. This signal dependant compression scheme was designed by a two-step process. The first (internal optimization) was the best basis selection that was performed for a given mother wavelet. For this purpose, three additive cost functions were applied and compared. The second (external optimization) was the selection of the mother wavelet based on the minimal distortion of the decoded signal given a fixed compression ratio. The mother wavelet was parameterized in the multiresolution analysis framework by the scaling filter, which is sufficient to define the entire decomposition in the orthogonal case. The method was tested on two sets of ten electromyographic (EMG) and ten electrocardiographic (ECG) signals that were compressed with compression ratios in the range of 50%-90%. For 90% compression ratio of EMG (ECG) signals, the percent residual difference after compression decreased from (mean +/- SD) 48.6 +/- 9.9% (21.5 +/- 8.4%) with discrete wavelet transform (DWT) using the wavelet leading to poorest performance to 28.4 +/- 3.0% (6.7 +/- 1.9%) with DWPT, with optimal basis selection and wavelet optimization. In conclusion, best basis selection and optimization of the mother wavelet through parameterization led to substantial improvement of performance in signal compression with respect to DWT and randon selection of the mother wavelet. The method provides an adaptive approach for optimal signal representation for compression and can thus be applied to any type of biomedical signal.     

NNERVE: Neural Network Extraction of Repetitive Vectors forElectromyography. I. Algorithm

Artificial neural network (ANN) based signal processing methods have been shown to have significant robustness in processing complex, degraded, noisy, and unstable signals. A novel approach to automated electromyogram (EMG) signal decomposition, using an ANN processing architecture, is presented here. Due to the lack of a priori knowledge of motor unit action potential (MUAP) morphology, the EMG decomposition must be performed in an unsupervised manner. An ANN classifier, consisting of a multilayer perceptron neural network and employing a novel unsupervised training strategy, is proposed. The ANN learns repetitive appearances of MUAP waveforms from their suspected occurrences in a filtered EMG signal in an autoassociative learning task. The same training waveforms are fed into the trained ANN and the output of the ANN is fed back to its input, giving rise to a dynamic retrieval net classifier. For each waveform in the data, the network discovers a feature vector associated with that waveform. For each waveform, classification is achieved by comparing its feature vector with those of the other waveforms. Firing information of each MUAP is further used to refine the classification results of the ANN classifier. Then, individual MUAP waveform shapes are derived and their firing tables are created     

Wavelet-based enhancement of lung and bowel sounds using fractal dimension thresholding--Part I: methodology

An efficient method for the enhancement of lung sounds (LS) and bowel sounds (BS), based on wavelet transform (WT), and fractal dimension (FD) analysis is presented in this paper. The proposed method combines multiresolution analysis with FD-based thresholding to compose a WT-FD filter, for enhanced separation of explosive LS (ELS) and BS (EBS) from the background noise. In particular, the WT-FD filter incorporates the WT-based multiresolution decomposition to initially decompose the recorded bioacoustic signal into approximation and detail space in the WT domain. Next, the FD of the derived WT coefficients is estimated within a sliding window and used to infer where the thresholding of the WT coefficients has to happen. This is achieved through a self-adjusted procedure that iteratively "peels" the estimated FD signal and isolates its peaks produced by the WT coefficients corresponding to ELS or EBS. In this way, two new signals are constructed containing the useful and the undesired WT coefficients, respectively. By applying WT-based multiresolution reconstruction to these two signals, a first version of the desired signal and the background noise is provided, accordingly. This procedure is repeated until a stopping criterion is met, finally resulting in efficient separation of the ELS or EBS from the background noise. The proposed WT-FD filter introduces an alternative way to the enhancement of bioacoustic signals, applicable to any separation problem involving nonstationary transient signals mixed with uncorrelated stationary background noise. The results from the application of the WT-FD filter to real bioacoustic data are presented and discussed in an accompanying paper.     

基于解析图像的小波变换光学载频干涉全息图相位重建方法

将解析图像和实数小波变换(WT)相结合应用到光学载频全息图分析中。首先对载频全息图进行希尔伯特变换构造解析图像,然后对解析图像进行WT,提取小波脊处对应的WT系数的相位信息即可得到载频全息图的相位信息。由于母小波优秀的空域局部化能力,使得因全息图边缘不连续引入的误差被限制在局部区域。同时,由于不需要人工滤波操作,所提方法一定程度上解决了载频全息图的频谱混叠问题。给出了严格的理论公式推导、计算机模拟和实验验证。     

Singularity characteristics of needle EMG IP signals

Clinical electromyography (EMG) interference pattern (IP) signals can reveal more diagnostic information than their constituents, the motor unit action potentials (MUAPs). Singularities and irregular structures typically characterize the mathematically defined content of information in signals. In this paper, a wavelet transform method is used to detect and quantify the singularity characteristics of EMG IP signals using the Lipschitz exponent (LE) and measures derived from it. The performance of the method is assessed in terms of its ability to discriminate healthy, myopathic and neuropathic subjects and how it compares with traditionally used Turns Analysis (TA) methods and a method recently developed by the authors, interscale wavelet maximum (ISWM). Highly significant intergroup differences were found using the LE method. Most of the singularity measures have a performance similar to that of ISWM and considerably better than that of TA. Some measures such as the ratio of the mean LE value to the number of singular points in the signal have considerably superior performance to both methods. These findings add weight to the view that wavelet analysis methods offer an effective way forward in the quantitative analysis of EMG IP signal to assist the clinician in the diagnosis of neuromuscular disorders.     

A model of the muscle-fiber intracellular action potentialwaveform, including the slow repolarization phase

Recent studies have shown that the slow repolarization phase or "negative afterpotential" of the intracellular muscle-fiber action potential (IAP) plays an important role in determining the shape of the extracellularly recorded motor-unit action potential (MUAP). This paper presents a model of the IAP waveform as the sum of a spike and an afterpotential, both represented by simple analytical expressions. The model parameters that specify the sizes of the spike and afterpotential are shown to be proportional to the quadrupole and dipole moments of the transmembrane current distribution associated with the spike of the wave of excitation. The model provides a computationally efficient method for simulating the MUAP, and it can be reliably inverted to estimate the model parameters from empirical IAP and MUAP waveforms.     

Automatic Decomposition of the Clinical Electromyogram

We describe a new, automatic signal-processing method (ADEMG) for extracting motor-unit action potentials (MUAP's) from the electromyographic interference pattern for clinical diagnostic purposes. The method employs digital filtering to select the spike components of the MUAP's from the background activity, identifies the spikes by template matching, averages the MUAP waveforms from the raw signal using the identified spikes as triggers, and measures their amplitudes, durations, rise rates, numbers of phases, and firing rates. Efficient new algorithms are used to align and compare spikes and to eliminate interference from the MUAP averages. In a typical 10-s signal recorded from the biceps brachii muscle using a needle electrode during a 20 percent-maximal isometric contraction, the method identifies 8-15 simultaneously active MUAP's and detects 30-70 percent of their occurrences. The analysis time is 90 s on a PDP-11/34A.     

希尔伯特-黄变换和小波变换用于谐波分析的比较研究

电力系统的谐波分析方法应该有良好的计算效率,并有良好的时域和频域分辨率。迄今为止,小波变换被广泛地应用于这个领域,但是小波基的选取等问题还需要进一步研究。近几年来,希尔伯特-黄变换的应用越来越多,该方法运用简便,而且并不涉及频率分辨率和时间分辨率的矛盾问题,是一个有很好应用前景的分析方法。把上述两种方法应用于电力系统的谐波分析,比较了两者的优缺点。结果表明,希尔伯特-黄变换有较好的计算效率,以及较好的时域和频域分辨率,但存在端点飞翼和瞬时频率轻微波动两个问题。     

基于Hermite插值的小波模极大值重构滤波的肌电信号消噪方法

为了消除混杂在肌电信号中的噪声,该文提出了基于Hermite插值的小波模极大值重构滤波的肌电信号消噪方法。该方法先对肌电信号进行小波分解;其次,根据小波系数的奇异性,利用信号与噪声模极大值在小波尺度上的不同变化特性,分离出信号与噪声;再次,用Hermite插值法重构小波系数;最后从重构的小波系数恢复成去噪后的信号。实验结果表明,Hermite插值的小波模极大值重构能有效地去除噪声,提高信噪比,且保留了肌电信号的细节信息,为肌电信号的特征提取和模式识别创造了良好的条件。     

Unsupervised pattern recognition for the classification of EMGsignals

The shapes and firing rates of motor unit action potentials (MUAPs) in an electromyographic (EMG) signal provide an important source of information for the diagnosis of neuromuscular disorders. In order to extract this information from EMG signals recorded at low to moderate force levels, it is required: i) to identify the MUAPs composing the EMG signal, ii) to classify MUAPs with similar shape, and iii) to decompose the superimposed MUAP waveforms into their constituent MUAPs. For the classification of MUAPs two different pattern recognition techniques are presented: i) an artificial neural network (ANN) technique based on unsupervised learning, using a modified version of the self-organizing feature maps (SOFM) algorithm and learning vector quantization (LVQ) and ii) a statistical pattern recognition technique based on the Euclidean distance. A total of 1213 MUAPs obtained from 12 normal subjects, 13 subjects suffering from myopathy, and 15 subjects suffering from motor neuron disease were analyzed. The success rate for the ANN technique was 97.6% and for the statistical technique 95.3%. For the decomposition of the superimposed waveforms, a technique using crosscorrelation for MUAP's alignment, and a combination of Euclidean distance and area measures in order to classify the decomposed waveforms is presented. The success rate for the decomposition procedure was 90%     

Asymptotic decorrelation of between-Scale Wavelet coefficients

In recent years there has been much interest in the analysis of time series using a discrete wavelet transform (DWT) based upon a Daubechies wavelet filter. Part of this interest has been sparked by the fact that the DWT approximately decorrelates certain stochastic processes, including stationary fractionally differenced (FD) processes with long memory characteristics and certain nonstationary processes such as fractional Brownian motion. It is shown that, as the width of the wavelet filter used to form the DWT increases, the covariance between wavelet coefficients associated with different scales decreases to zero for a wide class of stochastic processes. These processes are Gaussian with a spectral density function (SDF) that is the product of the SDF for a (not necessarily stationary) FD process multiplied by any bounded function that can serve as an SDF on its own. We demonstrate that this asymptotic theory provides a reasonable approximation to the between-scale covariance properties of wavelet coefficients based upon filter widths in common use. Our main result is one important piece of an overall strategy for establishing asymptotic results for certain wavelet-based statistics.     

An adaptive edge model in the wavelet domain for wavelet image coding

State-of-art wavelet coders owe their performance to smart ideas for exploiting inter and intra-band dependencies of wavelet coefficients. We claim that developing more efficient coders requires us to look at the main source of these dependencies; i.e., highly localized information around edges. This paper investigates the structural relationships among wavelet coefficients based on an idealized view of edge behavior, and proposes a simple edge model that explains the roots of existing dependencies. We describe how the model is used to approximate and estimate the significant wavelet coefficients. Simulations support its relevance for understanding and analyzing edge information. Specifically, model-based estimation within the space-frequency quantization (SFQ) framework increases the peak signal-to-noise ratio (PSNR) by up to 0.3 dB over the original SFQ coding algorithm. Despite being simple, the model provides valuable insights into the problem of edge-based adaptive modeling of value and location information in the wavelet domain.     

基于小波变换的空域相关法在肌电信号中的应用

为了消除混杂在肌电信号中的噪声,并保留信号的细节,提出了基于小波变换空域相关法的肌电信号消噪方法.文章首先对小波变换和空域相关滤波的基本理论进行了简要的概述,其次就空域相关滤波用于肌电信号的消噪过程进行了详细的分析.通过肌电信号的小波分解,用空域相关法分离信号与噪声,并给出了一种针对肌电信号各层噪声能量阈值的估计算法.实验结果表明,空域相关滤波较好的保留了肌电信号的边缘特征,为肌电信号的特征提取创造了良好的条件.     

Application of higher order statistics techniques to EMG signals to characterize the motor unit action potential

The electromyographic (EMG) signal provides information about the performance of muscles and nerves. At any instant, the shape of the muscle signal, motor unit action potential (MUAP), is constant unless there is movement of the position of the electrode or biochemical changes in the muscle due to changes in contraction level. The rate of neuron pulses, whose exact times of occurrence are random in nature, is related to the time duration and force of a muscle contraction. The EMG signal can be modeled as the output signal of a filtered impulse process where the neuron firing pulses are assumed to be the input of a system whose transfer function is the motor unit action potential. Representing the neuron pulses as a point process with random times of occurrence, the higher order statistics based system reconstruction algorithm can be applied to the EMG signal to characterize the motor unit action potential. In this paper, we report results from applying a cepstrum of bispectrum based system reconstruction algorithm to real wired-EMG (wEMG) and surface-EMG (sEMG) signals to estimate the appearance of MUAPs in the Rectus Femoris and Vastus Lateralis muscles while the muscles are at rest and in six other contraction positions. It is observed that the appearance of MUAPs estimated from any EMG (wEMG or sEMG) signal clearly shows evidence of motor unit recruitment and crosstalk, if any, due to activity in neighboring muscles. It is also found that the shape of MUAPs remains the same on loading.