Morphological undecimated wavelet decomposition for fault location on power transmission lines

This paper presents a novel morphological undecimated wavelet (MUDW) decomposition scheme for fault location on power transmission lines. The MUDW scheme is developed based on the morphological wavelet (MW) theory for both the extraction of transient features and noise reduction in signal processing. The analysis operators and the synthesis operator of MUDW strictly satisfy the pyramid condition. In this paper, the MUDW scheme is used to extract features from noise imposed fault-generated transient voltage and/or current signals of power transmission lines. The efficiency of the MUDW scheme used for noise reduction and the extraction of sudden changes in the transient signals are evaluated in simulation studies. The simulation results show that the fault location can be accurately detected in noisy environments.     

Speckle removal from SAR images in the undecimated wavelet domain

Speckle reduction is approached as a minimum mean-square error (MMSE) filtering performed in the undecimated wavelet domain by means of an adaptive rescaling of the detail coefficients, whose amplitude is divided by the variance ratio of the noisy coefficient to the noise-free one. All the above quantities are analytically calculated from the speckled image, the variance and autocorrelation of the fading variable, and the wavelet filters only, without resorting to any model to describe the underlying backscatter. On the test image Lena corrupted by synthetic speckle, the proposed method outperforms Kuan's local linear MMSE filtering by almost 3-dB signal-to-noise ratio. When true synthetic aperture radar (SAR) images are concerned, empirical criteria based on distributions of multiscale local coefficient of variation, calculated in the undecimated wavelet domain, are introduced to mitigate the rescaling of coefficients in highly heterogeneous areas where the speckle does not obey a fully developed model, to avoid blurring strong textures and point targets. Experiments carried out on widespread test SAR images and on a speckled mosaic image, comprising synthetic shapes, textures, and details from optical images, demonstrate that the visual quality of the results is excellent in terms of both background smoothing and preservation of edge sharpness, textures, and point targets. The absence of decimation in the wavelet decomposition avoids typical impairments often introduced by critically subsampled wavelet-based denoising.     

Denoising of the uterine EHG by an undecimated wavelet transform

The authors propose two original methods of denoising of the uterine electrohysterography (EHG) signal by wavelets. This external electrophysiological signal is corrupted by electronic, electromagnetic noises and by the remaining electrocardiogram of the mother. The interfering signals have overlapping spectra. Therefore, a classical filtering is unusable. Wavelets should be a very well-suited denoising tool. The first proposed method uses the algorithm “a trou” with nonsymmetrical filters. The computation is rapid and the results are satisfying compared to the classical denoising techniques. The second algorithm is an improvement of the first method. It uses orthogonal wavelets and the result of the thresholding corresponds to the average of all circulant shifts denoised by a decimated wavelet transform. Results are compared to traditional denoising algorithms by wavelet (orthogonal, maximally decimated). The proposed algorithms are more efficient on simulated signals as well as on uterine EHG     

小波分解和重构的光学可变图像融合研究

针对传统光学可变图像融合方法存在的融合效果差、噪声干扰严重等问题,提出小波分解和重构的光学可变图像融合方法.分析光学可变图像在不同区域的融合原理,获取光学可变图像的特征;采用小波变化的方法,对光学可变图像进行多尺度分解,提取不同频率的小波系数;采用小波阈值降噪方式,对光学可变图像进行降噪处理;通过融合准则选取融合子图像...     

非抽样双树复小波域的BPP-NMF图像融合

提出了一种非抽样双树复小波变换（UDT-CWT）与基于块主元旋转的非负矩阵分解（BPP-NMF）相结合的多聚焦图像融合算法。利用UDT-CWT具有完美的平移不变性及良好的方向选择性,首先对图像进行多尺度、多方向分解并得到低频子带和高频子带系数;然后对低频子带系数采用块主元旋转的非负矩阵分解的融合策略,高频系数则选用高斯加权区域能量与区域标准差一致性选择的融合准则。最后对融合后的系数进行UDT-CWT逆变换得到重构图像。选用多组多聚焦图像进行融合并对融合结果进行主观视觉、客观方面的评价。试验结果表明,该融合算法不仅具有良好的视觉效果,同时在客观评价指标也优于一般的融合策略,验证了该算法的有效性。     

Multiresolution wavelet decomposition of the seismocardiogram

The seismocardiogram (SCG) is a complex, nonstationary signal used for pathological analysis of cardiac vibratory activity. This article reports the results of multiresolution wavelet decomposition of SCGs for a normal male subject, pertaining to three different physiological conditions. Marked differences in certain sub-bands are discernible, which are undetectable in the time-domain alone     

Tomographic image reconstruction by eigenvector decomposition: its limitations and areas of applicability

This paper analyzes in detail the process of tomographic image reconstruction by pseudo-inversion of the blurring matrix of a PET imaging system. Eigenvector and eigenvalue decomposition is used as a method to evaluate the physical reasons for the ill-conditioned nature of the problem. It is shown that finding an accurate pseudo-inverse for even a modest PET array of 8 x 8 pixels is a difficult task for a computer with 48-bit mantissa. The problem is caused by the strong ambiguity with which the detector system measures the activity at each pixel. For a problem in which imaging with a complete detector ring is not possible, and in which invariance of the point response function cannot be maintained, the pseudo-inverse method of reconstruction is, however, shown to be very useful. Advantage is taken of the fact that the activitiy to be measured is localized in a single plane, without over-or underlying activity. A planar camera configuration yields very well conditioned matrices that are separable for a large number of useful cases. It is even possible to define pixel sizes which are considerably smaller than the detector size and solve the problem without a substantial increase in the noise magnification factor. Recognizing that the above application is equivalent to a case of very well defined time-of-flight (TOF) measurement, the simple initial PET study is reevaluated by inclusion of TOF information.     

A binary wavelet decomposition of binary images

We construct a theory of binary wavelet decompositions of finite binary images. The new binary wavelet transform uses simple module-2 operations. It shares many of the important characteristics of the real wavelet transform. In particular, it yields an output similar to the thresholded output of a real wavelet transform operating on the underlying binary image. We begin by introducing a new binary field transform to use as an alternative to the discrete Fourier transform over GF(2). The corresponding concept of sequence spectra over GF(2) is defined. Using this transform, a theory of binary wavelets is developed in terms of two-band perfect reconstruction filter banks in GF(2). By generalizing the corresponding real field constraints of bandwidth, vanishing moments, and spectral content in the filters, we construct a perfect reconstruction wavelet decomposition. We also demonstrate the potential use of the binary wavelet decomposition in lossless image coding.     

Optimal biorthogonal wavelet bases for signal decomposition

The selection of scaling functions for optimal signal representation by general multidimensional biorthogonal wavelet bases is investigated. Criterion for optimality is the minimization of the mean-square approximation error at each level of the decomposition. Conditions are given under which the approximation error of the decomposition approaches zero as the level increases. Given arbitrary synthesis filters, the optimal corresponding analysis filters are determined. Globally optimal families of filters are also found, and suboptimal linear and nonlinear-phase filters for the realization of the optimal scaling functions are explicitly determined     

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.     

Compressive sensing reconstruction via decomposition

When recovering images from a small number of Compressive Sensing (CS) measurements, a problem arises whereby image features (e.g., smoothness, edges, textures) cannot be preserved well in reconstruction, especially textures at small-scale. Since the missing information still remains in the residual measurement, we propose a novel Decomposition-based CS-recovery framework (DCR) which utilizes residual reconstruction and state-of-the-art filters. The proposed method iteratively refines residual measurement which is closely related to the denoise-boosting techniques. DCR is further incorporated with a weighted total variation and nonlocal structures in the gradient domain as priors to form the proposed Decomposition based Texture preserving Reconstruction (DETER). We subsequently demonstrate robustness of the proposed framework to noise and its superiority over the other state-of-the-art methods, especially at low subrates. Its fast implementation based on the split Bregman technique is also presented.     

Multiscale video representation using multiresolution motioncompensation and wavelet decomposition

A multiscale video representation using wavelet decomposition and variable-block-size multiresolution motion estimation (MRME) is presented. The multiresolution/multifrequency nature of the discrete wavelet transform makes it an ideal tool for representing video sources with different resolutions and scan formats. The proposed variable-block-size MRME scheme utilizes motion correlation among different scaled subbands and adapts to their importance at different layers. The algorithm is well suited for interframe HDTV coding applications and facilitates conversions and interactions between different video coding standards. Four scenarios for the proposed motion-compensated coding schemes are compared. A pel-recursive motion estimation scheme is implemented in a multiresolution form. The proposed approach appears suitable for the broadcast environment where various standards may coexist simultaneously     

基于小波分解和信息熵的涡结构识别方法

利用涡结构对光波通过高速流场的光学传输特性进行建模，就必须进行涡结构的识别。文中提出一种涡结构识别方法，首先把密度场转换的折射率场等效为具有丰富纹理信息的灰度图像，进而对其进行多小波分解，计算每次分解的小波基系数的熵值，利用阈值判定低熵的为大涡的小波基系数，高熵的为小涡的小波基系数。计算机仿真结果表明，该方法能有效地进行涡结构识别，为基于涡结构的光学传输精确建模奠定了基础。     

基于形态小波分解金字塔的图像融合

提出了一种基于形态小波分解的多分辨率图像融合.这种融合方法使用了最小形态小算子,将原始图像分解为4子带图像金字塔并且构造了相应的4子带方向对比度图像金字塔.然后利用方向对比度和区域标准差进行图像融合得到融合的4子带图像金字塔,最后应用形态小波重构得到融合图像.融合实验表明,本文方法优于传统的对比度金字塔图像融合和普通波分解图像融合.     

基于直方图散度和小波分解的图像配准算法

针对基于互信息的图像配准方法运行时间长、抗噪声差的问题,提出了一种基于新的相似性测度的图像配准算法,在分析两幅图像的联合直方图点集分布情况的基础上,定义了直方图点集的散度公式,并将其作为相似性测度.为加速参数的搜索过程,配准是在小波域内进行的,并使用遗传算法与Powell算法相结合的方法来优化参数.实验证明,相对于基于互信息的图像配准算法,本算法参数优化方法选择可以更灵活,时间消耗更少,噪声鲁棒性更优.     

Direct reconstruction method for wavelet transform extremarepresentation

In contrast to the iterative reconstruction algorithm of projections onto convex sets a noniterative method that completely solves the problem of reconstructing from the wavelet transform extrema representation is presented for the first time. The solution obtained by the proposed method is mathematically consistent and is indistinguishable from the true solution, i.e. both give the same representation. The proposed method consists of first finding a least-squares solution in the space spanned by the wavelet sampling bases. An orthogonal component that is to be added to the least-squares solution to form a consistent solution is then found by solving a set of linear inequalities specified by the a priori information in the representation using the linear programming technique. Numerical results presented show that the reconstructions are of good quality     

基于小波变换的图像重构算法研究

小波变换是当前图像处理、应用数学和工程学科中一个迅速发展的领域,它具有多分辨率分析的特性,同时又在变换域有表征信号局部特征的能力,能有效地从信号中提取信息。本课题以MATLAB作为平台,研究小波变换的mallet算法,对一维离散采样信号进行滤波和重采样,并扩展到多维信号中。根据算法结果,对图像进行小波分解,重构其近似信...     

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.     

Biorthogonal wavelet system for high-resolution image reconstruction

High-resolution images are often desired but made impossible because of hardware limitations. For the high-resolution model proposed by Bose and Boo (see Int. J. Imaging Syst. Technol., vol.9, p.294-304, 1998), the iterative wavelet-based algorithm has been shown to perform better than the traditional least square method when the resolution ratio M is two and four. In this paper, we discuss the minimally supported biorthogonal wavelet system that comes from the mathematical model by Bose and Boo and propose a wavelet-based algorithm for arbitrary resolution ratio M/spl ges/2. The numerical results indicate that the algorithm based on our biorthogonal wavelet system performs better in high-resolution image reconstruction than the wavelet-based algorithm in the literature, as well as the common-used least square method.