A new wavelet-based fuzzy single and multi-channel image denoising

In this paper, we propose a new wavelet shrinkage algorithm based on fuzzy logic. In particular, intra-scale dependency within wavelet coefficients is modeled using a fuzzy feature. This feature space distinguishes between important coefficients, which belong to image discontinuity and noisy coefficients. We use this fuzzy feature for enhancing wavelet coefficients' information in the shrinkage step. Then a fuzzy membership function shrinks wavelet coefficients based on the fuzzy feature. In addition, we extend our noise reduction algorithm for multi-channel images. We use inter-relation between different channels as a fuzzy feature for improving the denoising performance compared to denoising each channel, separately. We examine our image denoising algorithm in the dual-tree discrete wavelet transform, which is the new shiftable and modified version of discrete wavelet transform. Extensive comparisons with the state-of-the-art image denoising algorithm indicate that our image denoising algorithm has a better performance in noise suppression and edge preservation.     

一种基于曲线进化的医学图像解剖轮廓提取算法的研究

水平集方法应用于跟踪界面演化问题,是一种稳定有效的数值计算方法。图象小波变换模极大值对图象中目标轮廓边缘有很好的表征。论文应用水平集方法基于曲线进化提出了一种新的医学图像解剖轮廓分割算法,定义了一种基于小波变换模极大值的用于终止进化的函数,构造了一种基于领域的进化方式,并对脊柱MRI图象进行了分割实验,得到了令人鼓舞的结果。实验表明了该种算法的可行性和有效性。     

On the Numerical Solution of Some Semilinear Elliptic Problems – II

In the earlier paper [6], a Galerkin method was proposed and analyzed for the numerical solution of a Dirichlet problem for a semi-linear elliptic boundary value problem of the form –U=F(·,U). This was converted to a problem on a standard domain and then converted to an equivalent integral equation. Galerkins method was used to solve the integral equation, with the eigenfunctions of the Laplacian operator on the standard domain D as the basis functions. In this paper we consider the implementing of this scheme, and we illustrate it for some standard domains D.     

Chatter detection based on probability distribution of wavelet modulus maxima

This paper presents a statistical chatter detection method. The methodology is based on the study of discrete wavelet transform (DWT) scheme and statistical analysis of wavelet transform modulus maxima (WTMM). Wavelet transform modulus maxima is used to describe any point where wavelet transform of a signal is locally maximal at corresponding time location. Meanwhile, due to the noisy machining environment, a wavelet-based de-noising method including a hybrid thresholding function and a level-dependent universal threshold rule is proposed. A non-dimensional chatter index varying between 0 and 1 is designed based on the statistical analysis of the WTMM. The main advantages of the proposed chatter index include that: (a) its variation range is independent of process parameters and machining systems, and (b) its threshold value is much less susceptible to cutting condition changes since its value is in relative term. As a result, the chatter index could be used for different machining processes without the time-consuming recalibration process.     

Harmonic Wavelet Transform and Image Approximation

In 2006, Saito and Remy proposed a new transform called the Laplace Local Sine Transform (LLST) in image processing as follows. Let f be a twice continuously differentiable function on a domain Ω. First we approximate f by a harmonic function u such that the residual component v=f−u vanishes on the boundary of Ω. Next, we do the odd extension for v, and then do the periodic extension, i.e. we obtain a periodic odd function v ^*. Finally, we expand v ^* into Fourier sine series. In this paper, we propose to expand v ^* into a periodic wavelet series with respect to biorthonormal periodic wavelet bases with the symmetric filter banks. We call this the Harmonic Wavelet Transform (HWT). HWT has an advantage over both the LLST and the conventional wavelet transforms. On the one hand, it removes the boundary mismatches as LLST does. On the other hand, the HWT coefficients reflect the local smoothness of f in the interior of Ω. So the HWT algorithm approximates data more efficiently than LLST, periodic wavelet transform, folded wavelet transform, and wavelets on interval. We demonstrate the superiority of HWT over the other transforms using several standard images.     

小波变换在车流量检测雷达信号去噪中的应用

分析了车流量检测雷达中频信号的特点,探讨了小波变换在中频信号去噪中的应用;分别采用小波变换阈值法、平移不变量法和小波变换模极大值法对中频信号进行了去噪处理并对这三种方法的去噪性能进行了分析;实验结果表明,三种方法均能有效的抑制噪声,其中小波阈值法去噪效果较好,计算速度很快;平移不变量法去噪效果略优于小波阈值法,但计算速度较慢,模极大值法虽然取得了最好的去噪效果,但计算速度很慢;综合而言,小波变换阈值法最具实用价值。     

On computing derivatives forC 1 interpolating schemes: an optimization

The application of Powell-Sabin’s or Clough-Tocher’s schemes to scattered data problems, as known requires the knowledge of the partial derivatives of first order at the vertices of an underlying triangulation. We study alocal method for generating partial derivatives based on the minimization of the energy functional on the star of triangles sharing a node that we called acell. The functional is associated to some piecewise polynomial function interpolating the points. The proposed method combines theglobal Method II by Renka and Cline (cf. [16, pp. 230–231]) with the variational approach suggested by Alfeld (cf. [2]) with care to efficiency in the computations. The locality together with some implementation strategies produces a method well suited for the treatment of a big amount of data. An improvement of the estimates is also proposed.     

基于小波奇异性理论的输油管道泄漏检测与定位方法

将小波分析在模极大值处理中的优势应用到管道泄漏检测与定位信号分析中,根据信号小波变换模极大值和信号奇异性之间的关系,由小波变换模极大值沿尺度变化趋势分析出压力信号的突变点,计算出管道泄漏诱发的负压波传播到上下游监测点的时间差,利用负压波定位泄漏的常规公式确定出泄漏点的位置。实验证明,该方法能快速准确地捕捉压力信号突变点,并定位管道泄漏位置。     

一种改进的心电图QRS波群检测算法

在利用小波变换检测QRS波群时,最关键的部分就是模极值配对,提出一种区域极值配对算法来检测R波。首先利用二次样条小波基函数和多孔(ATrous)算法对心电(ECG)信号进行小波变换求取模极值,用正极大值来确定搜索区域,以这个正极大值为起点,以这个确定区域为搜索范围,向左搜索负极大值点,将这两个极值配对,他们之间的过零点就是R波的对应点,然后在检测到R波的基础上检测出Q波与S波,再结合距离最大值法检测出QRS波群的起止点。并采用医学相关理论对检测结果进行优化,进一步去除错检点,补偿漏检点。最后利用MIT-BIH心率失常数据库中记录的数据对该算法进行验证,实验结果表明所提算法能准确检测QRS波群,平均检出率达到了99.97%。     

Surfaces parametrized by the normals

For a surface with non vanishing Gaussian curvature the Gauss map is regular and can be inverted. This makes it possible to use the normal as the parameter, and then it is trivial to calculate the normal and the Gauss map. This in turns makes it easy to calculate offsets, the principal curvatures, the principal directions, etc. Such a parametrization is not only a theoretical possibility but can be used concretely. One way of obtaining this parametrization is to specify the support function as a function of the normal, i.e., as a function on the unit sphere. The support function is the distance from the origin to the tangent plane and the surface is simply considered as the envelope of its family of tangent planes. Suppose we are given points and normals and we want a C ^k -surface interpolating these data. The data gives the value and gradients of the support function at certain points (the given normals) on the unit sphere, and the surface can be defined by determining the support function as a C ^k function interpolating the given values and gradients.     

A stable algorithm for Hankel transforms using hybrid of Block-pulse and Legendre polynomials

A new numerical method, based on hybrid of Block-pulse and Legendre polynomials for numerical evaluation of Hankel transform is proposed in this paper. Hybrid of Block-pulse and Legendre polynomials are used as a basis to expand a part of the integrand, rf(r), appearing in the Hankel transform integral. Thus transforming the integral into a Fourier-Bessel series. Truncating the series, an efficient algorithm is obtained for the numerical evaluations of the Hankel transforms of order ν>−1. The method is quite accurate and stable, as illustrated by given numerical examples with varying degree of random noise terms εθi added to the data function f(r), where θi is a uniform random variable with values in [−1,1]. Finally, an application of the proposed method is given in solving the heat equation in an infinite cylinder with a radiation condition.     

小波变换在X射线图像边缘检测中的应用

分析了X射线探伤图像的特点,将小波变换技术应用到X射线图像的边缘检测中,提出了基于小波变换的模极大值边缘检测算法,利用二次B样条小波,采用Mallat快速算法进行小波分解,采用分块阈值选取方法确定模极大值点,给出缺陷边缘。实验结果表明,该方法去噪效果好,检测出的缺陷边缘具有较强的连续性。     

基于小波模极大值和Neyman-Pearson准则阈值的图像去噪

首先给出了2维噪声的小波变换特性,分析图像小波变换模的极大值与小波分解级数j和李氏指数之间的关系,指出如何确定和保护图像的边缘;接着阐述了基于软、硬阈值的图像正交小波变换去噪法,然后提出一种基于Neym an-Pearson准则的小波阈值的确定,从而又提出了一种基于小波模极大值和Neym an-Pearson准则阈值的图像去噪方法,解决了图像去噪和保护图像边缘这个“两难”问题。针对期望图像叠加了不规则噪声的假设,对几种去噪方法做了定性比较,并给出了去噪性能的定量分析,仿真结果表明,此方法能提高去噪后图像的信噪比,使评价原图像与去噪后的图像近似程度的方差和相对熵为最小,同时能很好地保留原始图像的边缘信息。     

基于小波模极大值的信号奇异性检测

小波分析近乎完美的数学特性受到各领域科学家和工程技术人员的青睐.文中讨论了基于小波模极大值的信号奇异性检测方法,该方法突破了傅立叶分析在时域和频域方面的局部化能力,信号的局部正则性可由其小波变换模随尺度参数的衰减特性来刻画,通过确定小波变换在细尺度下的局部模极大值来检测信号奇异性.实验表明,该方法能有效的、实用的.     

基于相邻尺度小波变换乘积的镜头渐变检测

镜头边界检测是进行视频内容分析的首要步骤。提出一种基于相邻尺度小波变换乘积的镜头边缘检测方法。对镜头内的每帧视频图像进行小波变换,求出各帧图像相邻尺度小波变换尺度积的模和方向。计算连续帧图像尺度积与模之间的绝对距离,得到2帧图像间的不连续值。通过自适应阈值分割,检测出镜头边界。     

基于小波系数相关性的图像篡改盲检测及定位

分析了小波变换模极大值与信号突变点之间存在的联系,以及图像信息相关性的强弱,实现对图像的篡改部分进行检测。由于对图像进行篡改操作之后,通常会在两幅图像的结合处出现突变点（或者奇异点）,形成强边缘。因此,利用小波变换的多分辨率分析,求得模极大值进行多项式曲线拟合的结果,根据拟合误差的大小对图像的强边缘进行检测定位,再通过图像分块之间相关性的强弱,对篡改区域进行更准确的篡改检测和定位分析。实验结果证明,该方法能够检测到篡改信息,并且可对图像中的篡改部分进行准确定位。     

基于小波模极大值的混合立体匹配算法的仿真

该文提出一种新的,利用小波模极大值的基于特征和区域的混合立体匹配算法。首先详细地叙述了如何利用小波模极大值提取图像边缘,并用该点的小波模极大值和幅角作为这些边缘点的特征描述。并在图像边缘立体匹配的过程中,将以前用于图像灰度域的互相关函数应用于小波域,边缘点的视差仿真图显示,该边缘匹配算法取得了很好的效果。然后,在基于区域的匹配中,利用边缘匹配的结果,减少了匹配互相关的搜索的范围,大大减少了计算量,增加了正确率。最后,将两个视差图结合起来,就得到了最终的稠密的视差图。     

Smoothing transforms for wavelet approximation of piecewise smooth functions

Multi-resolution analysis with high vanishing moment wavelets provides a framework to efficiently approximate smooth functions. However, it is a well-known fact that wavelet approximation usually cannot achieve the same order of approximation in the vicinity of discontinuous points of functions as that in the smooth regions. Ringing artefacts in the reconstructed functions inevitably appear around discontinuous points. To reduce these artefacts, the authors propose to locally smooth piecewise smooth functions at the discontinuous points, prior to applying the wavelet transform, via a smoothing transform. The numerical experiments for one- and two-dimensional signals show the effectiveness of the proposed strategy.     

A fusion estimation method based on fractional Fourier transform

Image denoising methods have different denoising performance in both spatial and transform domains, and each method has its relative advantages and inherent shortcomings compared with other methods. A very intuitive idea is to find that an effective fusion method that can combine with the advantages of different denoising methods. In this paper, we propose a novel fusion method based on the fractional Fourier transform and apply it to image denoising problem. Our method is mainly divided into three steps: Firstly, a pre-estimation is made by any two denoising method separately in the spatial domain. Secondly, using these two estimated results as well as their Fourier transform, twice Fourier transform and three times Fourier transform, we obtain a fused result in the fractional Fourier transform domain. Thirdly, the inverse fractional Fourier transform and the modulus operation are used to obtain the final fusion result. Obviously, this approach is the fusion method in four different domains. Experimental results on benchmark test images demonstrate that the proposed method outperforms state-of-the-art stand-alone methods as: BM3D, DDID, MLP, EPLL and also superior to the fusion methods such as classic wavelet fusion method, PCA fusion method and the state-of-the-art CIEM fusion method in terms of quantity value such as the peak signal to noise ratio (PSNR), the structural similarity (SSIM), and visual quality.