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.     

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.     

Entropy-based optimization of wavelet spatial filters

A new class of spatial filters for surface electromyographic (EMG) signal detection is proposed. These filters are based on the 2-D spatial wavelet decomposition of the surface EMG recorded with a grid of electrodes and inverse transformation after zeroing a subset of the transformation coefficients. The filter transfer function depends on the selected mother wavelet in the two spatial directions. Wavelet parameterization is proposed with the aim of signal-based optimization of the transfer function of the spatial filter. The optimization criterion was the minimization of the entropy of the time samples of the output signal. The optimized spatial filter is linear and space invariant. In simulated and experimental recordings, the optimized wavelet filter showed increased selectivity with respect to previously proposed filters. For example, in simulation, the ratio between the peak-to-peak amplitude of action potentials generated by motor units 20 degrees apart in the transversal direction was 8.58% (with monopolar recording), 2.47% (double differential), 2.59% (normal double differential), and 0.47% (optimized wavelet filter). In experimental recordings, the duration of the detected action potentials decreased from (mean +/- SD) 6.9 +/- 0.3 ms (monopolar recording), to 4.5 +/- 0.2 ms (normal double differential), 3.7 +/- 0.2 (double differential), and 3.0 +/- 0.1 ms (optimized wavelet filter). In conclusion, the new class of spatial filters with the proposed signal-based optimization of the transfer function allows better discrimination of individual motor unit activities in surface EMG recordings than it was previously possible.     

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     

An equalization algorithm for wavelet packet based modulationschemes

A considerable amount of attention has been given in the literature to the use of wavelets for modulation and equalization. In this correspondence, we present an equalization algorithm for a wavelet packet-based modulation scheme. A nonideal channel can be divided into a set of bands, where each band can be approximated as a simple attenuation and delay channel. Wavelet packets, being narrowband and orthonormal, are a natural choice for realizing such bands. Thus, if the data sequence is used to modulate a set of wavelet packets, the equalization problem reduces to that of determining the delay introduced by the channel for each of the wavelet packets (if the wavelet packets do not overlap in the frequency domain) and possibly a change of sign in the decoded symbols. The attenuation affects the SNR at the output of the demodulator, which in turn affects the correct decoding of the transmitted symbols. A minimum square variance algorithm for adaptively choosing the delay has been proposed. The algorithm uses the statistics of the received sequence to pick the appropriate delay. Simulations have been conducted to study the performance of the equalization algorithm and compare it with that of DFT-based DMT scheme     

Sharing secret images using integer single or multiple wavelet transform

Integer wavelet transform or multiple wavelet transform has been found attractive in image and video applications where its scaling function(s) and wavelet(s) provide higher energy compaction in smooth (scaling) subband and smaller values of detail (wavelet) coefficients. This paper presents a study on an image sharing method applying the integer single or multiple wavelet transform and Shamir’s (r, m) threshold scheme that provide highly compact and easily manageable shadows for real time progressive transmission. Experimental results are given to illustrate the characteristics of this method.     

An effective wavelet matrix transform approach for efficientsolutions of electromagnetic integral equations

An effective numerical method based on wavelet matrix transforms for efficient solution of electromagnetic (EM) integral equations is proposed. Using the wavelet matrix transform produces highly sparse moment matrices which can be solved efficiently. A fast construction method for various orthonormal or nonorthonormal wavelet basis matrices is also given. It has been found that using nonsimilarity wavelet matrix transforms such as nonsimilarity nonorthonormal cardinal spline wavelet (NSNCSW) transform, one can obtain a much higher compression rate and much better accuracy of the approximate solutions than using similarity wavelet transforms such as Daubechies' (1992) orthonormal wavelet (DOW) transform. Numerical examples are given to show the validity and effectiveness of the method     

Satellite image compression by concurrent representations of wavelet blocks

This paper proposes a complete compression and coding scheme for on-board satellite applications considering the main on-board constraints: low computational power and easy bit rate control. The proposed coding scheme improves the performance of the current Consultative Committee for Space Data Systems (CCSDS) recommendation for a low additional complexity. We consider post-transforms in the wavelet domain, select the best representation for each block of wavelet coefficients, and encode it into an embedded bit stream. After applying a classical wavelet transform of the image, several concurrent representations of blocks of wavelet coefficients are generated. The best representations are then selected according to a rate-distortion criterion. Finally, a specific bit-plane encoder derived from the CCSDS recommendation produces an embedded bit stream ensuring the easy rate control required. In this article, both the post-transforms and the best representation selection have been adapted to the low complexity constraint, and the CCSDS coder has been modified to compress post-transformed representations.     

基于小波变换的光寻址电位传感器信号去噪研究

基于(LAPS)(光寻址电位传感器)技术的生化传感器中的光生电流是一种微弱的非平稳信号,信噪比(SNR)低。为了提取清晰的LAPS信号,且鉴于传统的傅里叶方法去噪后信号失真严重,本文采用小波变换的方法对LAPS信号进行去噪处理。通过小波变换将信号分解为3层,得到各层的小波系数以及阈值。根据每一层系数特点,按阈值进行分别处理,得到新的小波系数。最后根据新的小波系数,重构信号。对去噪后的信号进行频谱分析发现,信号频谱为有效的LAPS信号谱段。将傅里叶去噪和小波去噪方法进行对比发现,小波去噪得到信号的SNR和平滑度(SR)要高于傅里叶去噪,表明小波变换是LAPS信号去噪的有效方法。     

Hierarchical quantization indexing for wavelet and wavelet packet image coding

In this paper, we introduce the quantization index hierarchy, which is used for efficient coding of quantized wavelet and wavelet packet coefficients. A hierarchical classification map is defined in each wavelet subband, which describes the quantized data through a series of index classes. Going from bottom to the top of the tree, neighboring coefficients are combined to form classes that represent some statistics of the quantization indices of these coefficients. Higher levels of the tree are constructed iteratively by repeating this class assignment to partition the coefficients into larger subsets. The class assignments are optimized using a rate-distortion cost analysis. The optimized tree is coded hierarchically from top to bottom by coding the class membership information at each level of the tree. Context-adaptive arithmetic coding is used to improve coding efficiency. The developed algorithm produces PSNR results that are better than the state-of-art wavelet-based and wavelet packet-based coders in literature.     

Semi-orthogonal versus orthogonal wavelet basis sets for solvingintegral equations

The two categories of wavelets, orthogonal and semi-orthogonal, are compared and it is shown that the semi-orthogonal wavelet is best suited for integral equation applications. The Battle-Lemarie orthogonal wavelet and the spline generated semi-orthogonal wavelet are each used to solve for the current distribution on an infinite strip illuminated by a transverse magnetic (TM) plane wave and a straight thin wire illuminated by a normally incident plane wave. The grounds for comparison are accuracy in characterizing the current, matrix sparsity, computation time, and singularity extraction capability. The limitations and advantages of solving integral equations with each of the two wavelet categories are discussed     

Spatial adaptive Bayesian wavelet threshold exploiting scale and space consistency

Threshold selection is critical in image denoising via wavelet shrinkage. Many powerful approaches have been investigated, but few of them are adaptive to the changing statistics of each subband and meanwhile keep efficiency of the algorithm. In this work, an inter-scale adaptive, data-driven threshold for image denoising via wavelet soft-thresholding is proposed. To get the optimal threshold, a Bayesian estimator is applied to the wavelet coefficients. The threshold is based on the accurate modeling of the distribution of wavelet coefficients using generalized Gaussian distribution (GGD), and the near exponential prior of the wavelet coefficients across scales. The new approach outperforms BayesShrink because it captures the statistical inter-scale property of wavelet coefficients, and is more adaptive to the data of each subband. The simplicity of the proposed threshold makes it easy to achieve the spatial adaptivity, which will further improves the wavelet denoising performance. Simulation results show that higher peak-signal-to-noise ratio can be obtained than other thresholding methods for image denoising.     

The phaselet transform-an integral redundancy nearly shift-invariant wavelet transform

This paper introduces an approximately shift invariant redundant dyadic wavelet transform - the phaselet transform - that includes the popular dual-tree complex wavelet transform of Kingsbury (see Phil. R. Soc. London A, Sept. 1999) as a special case. The main idea is to use a finite set of wavelets that are related to each other in a special way - and hence called phaselets - to achieve approximate shift-redundancy; the bigger the set, the better the approximation. A sufficient condition on the associated scaling filters to achieve this is that they are fractional shifts of each other. Algorithms for the design of phaselets with a fixed number vanishing moments is presented - building on the work of Selesnick (see IEEE Trans. Signal Processing) for the design of wavelet pairs for Kingsbury's dual-tree complex wavelet transform. Construction of two-dimensional (2-D) directional bases from tensor products of one-dimensional (1-D) phaselets is also described. Phaselets as a new approach to redundant wavelet transforms and their construction are both novel and should be interesting to the reader, independent of the approximate shift invariance property that this paper argues they possess.     

Theory of regular M-band wavelet bases

Orthonormal M-band wavelet bases have been constructed and applied by several authors. This paper makes three main contributions. First, it generalizes the minimal length K-regular 2-band wavelets of Daubechies (1988) to the M-band case by deriving explicit formulas for K-regular M-band scaling filters. Several equivalent characterizations of K-regularity are given and their significance explained. Second, two approaches to the construction of the (M-1) wavelet filters and associated wavelet bases are described; one relies on a state-space characterization with a novel technique to obtain the unitary wavelet filters; the other uses a factorization approach. Third, this paper gives a set of necessary and sufficient condition on the M-band scaling filter for it to generate an orthonormal wavelet basis. The conditions are very similar to those obtained by Cohen (1990) and Lawton (1990) for 2-band wavelets     

Optimization of wavelet decomposition for image compression and feature preservation

A neural-network-based framework has been developed to search for an optimal wavelet kernel that can be used for a specific image processing task. In this paper, a linear convolution neural network was employed to seek a wavelet that minimizes errors and maximizes compression efficiency for an image or a defined image pattern such as microcalcifications in mammograms and bone in computed tomography (CT) head images. We have used this method to evaluate the performance of tap-4 wavelets on mammograms, CTs, magnetic resonance images, and Lena images. We found that the Daubechies wavelet or those wavelets with similar filtering characteristics can produce the highest compression efficiency with the smallest mean-square-error for many image patterns including general image textures as well as microcalcifications in digital mammograms. However, the Haar wavelet produces the best results on sharp edges and low-noise smooth areas. We also found that a special wavelet whose low-pass filter coefficients are 0.32252136, 0.85258927, 1.38458542, and -0.14548269) produces the best preservation outcomes in all tested microcalcification features including the peak signal-to-noise ratio, the contrast and the figure of merit in the wavelet lossy compression scheme. Having analyzed the spectrum of the wavelet filters, we can find the compression outcomes and feature preservation characteristics as a function of wavelets. This newly developed optimization approach can be generalized to other image analysis applications where a wavelet decomposition is employed.     

Power spectral density estimation via wavelet decomposition

A soft decision algorithm for wavelet decomposition, in which a probability measure is assigned to each frequency band bearing energy, is presented. This soft decision algorithm is used as an approximate estimator of power spectral density. A staircase approximation of power spectral density (PSD) is obtained by plotting the 2/sup m/ probabilities after an m-stage decomposition. Different wavelet filters are used for estimating the PSD of a speech segment. The type of the wavelet filter used can be selected as a compromise between accuracy and complexity.     

Feldkamp-type cone-beam tomography in the wavelet framework

X-ray computed tomography (CT) is in transition from fan-beam to cone-beam geometry. For cone-beam volumetric imaging, reduction of radiation exposure remains an important issue. Because the wavelet approach was shown to be effective and flexible for two-dimensional (2-D) local region reconstruction, we are motivated to perform wavelet local CT in cone-beam geometry. In this paper, we formulate the Feldkamp cone-beam reconstruction from the wavelet perspective, derive both full-scan and half-scan Feldkamp-type formulas for either global or local reconstruction, and demonstrate the feasibility and utility in synthetic and real data. It is found that using the wavelet Feldkamp approach, a three-dimensional (3-D) region of interest (ROI) can be reconstructed with neither severe image artifacts nor any significant constant bias in our simulation and experiments.     

From the wavelet series to the discrete wavelet transform-theinitialization

The discrete wavelet transform (DWT) is computed by subband filters bank and often used to approximate wavelet series (WS) and continuous wavelet transform (CWT). The approximation is often inaccurate because of improper initialized discretization of the continuous-time signal. In this correspondence, the problem is analyzed, and two simple algorithms for the initialization are introduced. Finally, numerical examples are presented to show that our algorithms are more effective than others     

一种新的小波可视电话编码算法

针对极低比特率应用提出一种新的结合H.263与SLCCA的混合小波视频编码算法。在提出的算法中,首先,用基于H.263的微调运动估计减小时间冗余,用无遗漏覆盖块运动补偿保证运动补偿误差帧的连续性;第二,对运动补偿误差帧进行小波变换得到全局能量压缩;第三,用SLCCA组织和表示小波变换后的数据,最后,运动向量的水平和垂直分量分别用自适应算法编码,算法在A级测试序列Akiyo和B级测试序列Foreman（QFIF）上测试取得了良好效果。     

Analysis of electromagnetic scattering from conducting bodies ofrevolution using orthogonal wavelet expansions

The wavelet expansion method has been extended to study the electromagnetic scattering from conducting bodies of revolution. The magnetic field integral equation (MFIE) is solved by this approach. By expanding the induced surface currents in terms of Fourier series of uncoupled azimuthal cylindrical modes, a simplified MFIE is attained for each unknown mode current that varies along the curved profile of the scatterer. By applying the boundary element method (BEM), the curved profile is mapped into the definition domain of the orthogonal wavelets on the interval. The unknown mode currents are then expressed using multiscale wavelet expansions. The simplified MFIE is converted into a sparse, multilevel matrix equation by the Galerkin method. Numerical examples are provided to illustrate the merits of this wavelet approach