基于三角样条小波变换和三角样条插值信号重构方法

文献8使用二进小波变换提取信号边缘特征,根据信号特征点的值和导数值用三次埃米特多项式进行插值重构。该文分析了文献8存在的两个问题,并针对这两个问题进行改进,即在二进小波变换和插值重构时使用同一种函数———三角样条小波函数,这样才能体现出信号处理的本质。文章作者曾提出的三角样条小波正好同时具有作为小波函数和插值函数双重作用,大大提高信号重构质量。就信噪比和相对误差两项指标与Mallat算法和文献8算法进行了比较,效果明显。     

中心B样条二进小波多尺度边缘提取

分析了截尾的Canny算子在多尺度边缘提取时对运算速度造成的影响,提出了中 心B样条二进小波多尺度边缘提取,详尽地研究了Canny算子与中心B样条函数的若干性 质,中心B样条函数具有紧支集,以极快的速度逼近高斯函数,四阶中心B样条函数的导数 比Canny算子更接近最佳边缘检测滤波器.四阶中心B样条函数是二阶平滑问题的唯一最 优解,并且它的时频测不准关系值非常接近时频测不准关系下界.从对计算结果的讨论中也 得出中心B样条二进小波优于Canny算子的结论.     

Construction for a class of smooth wavelet tight frames

From the inequality |P(z)|2 + |P(-z)|2 ≤1, assuming that both of the low-pass filters and high-pass filters are unknown, we design compactly supported wavelet tight frames. The unknowing of low-pass filters allows the design more freedom, and both the low-pass filters and high-pass filters have symmetries or anti-symmetries. We give the algorithm for filters with odd and even lengths separately, some concrete examples of wavelet tight frames with the length 4, 5, 6, 7, and at last we give the result of decomposing Lena image with them.     

基于自适应二进小波变换的人脸检测方法

提出一种基于提升二进小波变换的检测人脸部位（如鼻子、眼睛和嘴唇等）的快速算法。在提升二进小波滤波器中的自由参数是学习的,从便使两个向量（其中一个向量的分量是提升二进小波滤波器系数,另一个向量的分量是人脸某部位像素）之间的夹角的余弦值最大化。学习得到的滤波器应用到测试图像中,可以检测人脸某些部位。实验结果表明,该方法具有较强的鲁棒性,能够很好地解决复杂背景下的人脸检测问题。由于该方法实现的简单性,并容易由硬件实现,使得检测速度进一步提高,因此该方法在可视电话等领域有着广阔的应用前景。     

Time–frequency localized three-band biorthogonal wavelet filter bank using semidefinite relaxation and nonlinear least squares with epileptic seizure EEG signal classification

In this paper, we design time–frequency localized three-band biorthogonal linear phase wavelet filter bank for epileptic seizure electroencephalograph (EEG) signal classification. Time–frequency localized analysis and synthesis low-pass filters (LPF) are designed using convex semidefinite programming (SDP) by transforming a nonconvex problem into a convex SDP using semidefinite relaxation technique. Three-band parameterized lattice biorthogonal linear phase perfect reconstruction filter bank (BOLPPRFB) is chosen and nonlinear least squares algorithm is used to determine its parameters values that generate the designed analysis and synthesis LPF such that the band-pass and high-pass filters are also well localized in time and frequency domain. The designed analysis and synthesis three-band wavelet filter banks are compared with the standard two-band filter banks like Daubechies maximally regular filter banks, Cohen–Daubechies–Feauveau (CDF) biorthogonal filter banks and orthogonal time–frequency localized filter banks. Kruskal–Wallis statistical test is employed to measure the statistical significance of the subband features obtained from the various two and three-band filter banks for epileptic seizure EEG signal classification. The results show that the designed three-band analysis and synthesis filter banks both outperform two-band filter banks in the classification of seizure and seizure-free EEG signals. The designed three-band filter banks and multi-layer perceptron neural network (MLPNN) are further used together to implement a signal classifier that provides classification accuracy better than the recently reported results for epileptic seizure EEG signal classification.     

一种利用系统状态方程构造小波的方法

当使用小波解决问题时,得到的结果与所选用的小波有较大的关系.如何针对特定的问题来构造适用的小波还没有有效的方法.阐述了一种利用消失矩条件和线性时不变系统的状态方程来构造小波的方法.为此首先简要的介绍了Diophantine方程和消失矩条件,然后利用系统的模式函数可以从解状态方程的特征根得到的特性,通过添加令小波与模式函数正交的条件,得到了构造小波的方法.并进一步对用所推导的方法构造双正交关于0对称的实小波这一具体情况进行了讨论.最后给出了应用此方法构造小波的一个实际的例子.     

有限长度信号Mallat算法的边界延拓方法

处理有限长度信号时需要对其边界做某种延拓处理.本文在对Mallat算法分析的基础上,研究了有限长度信号Mallat算法中常用的4种边界延拓方法,并详细推导了4种边界延拓方法实现小波变换的一般过程.详细讨论了对称延拓中的2种延拓方式,分别就滤波器长度和信号长度为奇数或偶数的情况进行了研究.在周期延拓和对称延拓中,为了使多级分解与重构顺利进行,引入一个二元标示序列,使得小波变换便于编程实现.最后以bior4.4双正交小波给出实例,计算结果表明,在保持信号长度不变的情况下,按本文延拓方法能实现完全重构.     

Mammogram Enhancement Using Lifting Dyadic Wavelet Transform and Normalized Tsallis Entropy

In this paper, we present a new technique for mammogram enhancement using fast dyadic wavelet transform （FDyWT） based on lifted spline dyadic wavelets and normalized Tsallis entropy. First, a mammogram image is decom- posed into a multiscale hierarchy of low-subband and high-subband images using FDyWT. Then noise is suppressed using normalized Tsallis entropy of the local variance of the modulus of oriented high-subband images. After that, the wavelet coefficients of high-subbands are modified using a non-linear operator and finally the low-subband image at the first scale is modified with power law transformation to suppress background. Though FDyWT is shift-invariant and has better poten- tial for detecting singularities like edges, its performance depends on the choice of dyadic wavclcts. On the other hand, the nulnber of vanishing moments is an important characteristic of dyadic wavelets for singularity analysis because it provides an upper bound measurement for singularity characterization. Using lifting dyadic schemes, we construct lifted spline dyadic wavelets of different degrees with increased number of vanishing moments. We also examine the effect of these wavelets on mammogram enhancement. The method is tested on mammogram images, taken from MIAS （Mammographic Image Analysis Society） database, having various background tissue types and containing different abnormalities. The comparison with tile state-of-the-art contrast enhancement methods reveals that the proposed method performs better and the difference is statistically significant.     

基于提升框架的M通道小波滤波器的构造

提升框架的核心思想是通过有限步预测和更新来构造小波滤波器。由于小波的多相位矩阵可以分解为多个矩阵的乘积，因此这些矩阵可以被看作是预测算子和更新算子。本文根据M通道小波变换理论，给出了基于提升框架下的M通道小波变换所对应的滤波器库的构造方法。与传统的方法不同，利用提升框架构造的任何滤波器库都自动满足精确重构性，所设计的预测滤波器满足N阶对偶消失矩，所设计的更新滤波器满足N阶基本消失矩，并给出了具体例子。     

一种新型双正交小波滤波器的设计

本文提出了一种从对称正则滤波器中得到一系列对称双正交小波的新技术,其主要思路是找出所给出滤波器的一个对称互补正则滤波器,这样得到的滤波器与理想半谱带滤波器之间存在最小二次方振幅偏差。因此,从给出的正则对称滤波器,或者从已知的对称双正交小波,都可以很容易得到一系列带有更好频率选择特性的对称双正交小波滤波器组。一旦找到互补滤波器,此互补滤波器的另外一个互补滤波器也就可以以同样的方法得到。系列双正交小波滤波器源自于标准An-otonini9/7双正交小波。应用此小波滤波器来压缩著名的Lena、Barbara和Goldhill等图像,改善了峰值信噪比(PSNR)。     

基于小波变换的图像压缩感知

针对图像变换后系数采样数量和图像重建质量之间的矛盾,从图像的结构和纹理特性出发,提出基于小波变换的图像压缩感知算法.讨论图像经过多尺度小波变换后系数的稀疏性,保留图像变换后的低频系数,只对高频系数进行测量,同时利用正交匹配追踪算法重构高频系数.实验仿真结果表明,该算法能有效提高图像重建质量.     

Filtering for texture classification: a comparative study

In this paper, we review most major filtering approaches to texture feature extraction and perform a comparative study. Filtering approaches included are Laws masks (1980), ring/wedge filters, dyadic Gabor filter banks, wavelet transforms, wavelet packets and wavelet frames, quadrature mirror filters, discrete cosine transform, eigenfilters, optimized Gabor filters, linear predictors, and optimized finite impulse response filters. The features are computed as the local energy of the filter responses. The effect of the filtering is highlighted, keeping the local energy function and the classification algorithm identical for most approaches. For reference, comparisons with two classical nonfiltering approaches, co-occurrence (statistical) and autoregressive (model based) features, are given. We present a ranking of the tested approaches based on extensive experiments     

基于Mallat算法的图像边界问题的研究

首先介绍了一维信号边界对称延拓方式及图像双正交小波分解重构算法，然后在一维信号边界延拓方式的基础上，研究了当高、低通滤波器长度为偶数，且关于1／2对称时，图像能够精确重构的边界延拓问题，并给出了图像的小波变换及边界对称延拓的步骤。最后，通过仿真实例验证了该对称边界延拓方式能够保证图像在小渡变抉中精确重构。     

Multiresolutions numerically from subdivisions

In previous work we introduced a construction to produce multiresolutions from given subdivisions. A portion of that construction required solving bilinear equations using a symbolic algebra system. Here we replace the bilinear equations with a pair of linear equation systems, resulting in a completely numerical construction. Diagrammatic tools provide assistance in carrying this out. The construction is shown for an example of univariate subdivision. The results for a bivariate subdivision are given to illustrate the construction's ability to handle multivariate meshes, as well as special points, without requiring any modification of approach. The construction usually results in analysis and reconstruction filters that are finite, since it seeks each filter locally for the neighborhood of the mesh to which it applies. The use of a set of filters constructed in this way is compared with filters based on spline wavelets for image compression to show that the construction can yield satisfactory results.     

小波变换极大值在数据压缩中的应用

传统利用小波变换进行数据压缩的方法是基于小波变换的多分辨率滤波技术。结合小波变换的多分辨率特性,提出利用二阶样条小波变换模极大值压缩数据的方法。并在此基础上采用设定阈值消除幅值比较小的模极大值点的方法对信号进一步压缩。理论和仿真表明,利用小波变换模极大值压缩比率大、重构精确,对于平稳信号更是可以获得传统方法无可比拟的极大压缩比。     

小波变换点对称边界延拓问题研究

比较了几种小波变换的边界延拓方式,对小波变换的点对称延拓进行了边界点的光滑性分析,提出基于奇数长对称小波变换的点对称延拓方式,并证明了它在保持信号数据量不变的情况下是可以完全重构的。对一段有限信号分别采用对称延拓和点对称延拓进行小波分解重构计算,结果表明点对称延拓的重构精度比对称延拓的高。     

基于提升格式的紧支集双正交小波的设计

通过研究提升格式构造完全重构滤波器的方法,并结合传统的双正交小波的构造理论,得到了构造基于提升格式的双正交紧支集小波的方法。同时列举滤波器长度为4-4,消失矩为2-1的基于提升格式的双正交小波的构造实例。将所构造出的小波实例用于信号和图像消噪,发现在滤波器长度相同的前提下,基于提升格式的小波的消噪效果优于普通小波,并且用自适应的方法在已求得的范围内找出达到最佳消噪效果的自由变量的取值。     

基于二进小波变换的多尺度图切割方法

针对传统多尺度图切割方法进行图像边缘轮廓提取时仅采用高斯低通滤波和一阶微分求导,而忽略轮廓精度的缺陷,提出利用二进小波变换的方法进行多尺度边缘检测。在建立多尺度相似矩阵的过程中,根据每层小波的特性直接对各个尺度的相似矩阵进行构造,有效地减少了求解相似矩阵的运算复杂度,降低了内存消耗。实验结果表明,该方法与传统多尺度图切割方法相比具有更好的分割效果。     

关于数字图像压缩中小波基选择问题的探讨

针对数字图像压缩编码中最优小波基的选择问题,论证了双正交样条小波基的优点,并对其进行了推导.样条小波的导数连续性保证了小波基的光滑性,双正交对偶小波的对称性使得滤波器具有线性相位,可减小失真,保证重构图像的质量.     

子带图象编码系统中对称扩展方法的研究

在子带图象编码系统中,有限长度信号序列（如图象信号）,存在由线性卷积引起的边界扩展效应。传统方法一般用圆卷积和对称扩展方法来减弱边界扩展效应,但实验结果表明边界还存在失真。为此,按序列中每个周期的长度和对称中心的位置不同,将对称周期序列分为4种情况,并分别研究它们在图象子带编码中的对称扩展方法。实验结果表明,按这种对称扩展方法能使重构信号在边界处不存在任何失真。