一种基于二进提升方案的医学图像增强

通过分析和研究二进提升方案,得到一种新的提升二进小波滤波器的构造方法.以新的B-样条二进小波作为初始二进小波滤波器,结合二维6 trous算法对原始医学图像进行多层分解,根据分解后系数特点,一方面对不同级数的高频系数利用单阈值和双阈值函数增强,对低频子带系数用线性拉升来扩大图像的整体对比度.另一方面结合消失矩条件,调整滤波器的提升参数,构造了具有线性相位、紧支撑、高阶消失矩及有限长的单位脉冲响应的提升二进小波,并将其与初始二进小波滤波器增强后图像进行比较.仿真结果表明提升后的滤波器对于对比度低、弱光照图像比初始滤波器的增强效果有了进一步提高,噪声放大问题有明显改善,更好地突出图像边缘特征、保留了图像更多细节信息.     

一种新的双正交小波的构造方法研究

在二进提升方案相关理论的基础上,结合双正交性、消失矩性和对称性条件,提出一种构造提升双正交小波的新方法.此方法从二进小波出发,考虑小波所具有的特性,通过选取适当的提升参数,具体构造了具有紧支撑、对称性、高阶消失矩和速降性的提升双正交小波.     

二进小波变换的卷积定理

本文研究二进小波变换在信号处理中的应用.首先证明了两个满足容许性条件和规范性条件的二进小波的卷积和相关仍满足容许性和规范性条件,然后证明了二进小波变换的卷积定理和相关性定理,最后给出数值例子说明二进小波变换的卷积定理在加噪信号重构中的优越性.     

框架提升的两种方案

该文给出了框架提升的两种方案,这两种方案能够使作者对已有的二进小波框架或滤波器进行修正从而构造出新的小波框架.特别地,这两种方案能够使作者从分段线性的样条紧框架的张量积出发设计出不可分框架,新的框架能起到π/4的整数倍方向上的加权平均算子、Sobel算子和Laplacian算子的作用.     

一类二次保形拟插值函数的研究

通过讨论一种保形拟插值的基函数与二次规范B-样条函数之间的关系,提出了一类二次保形拟插值样条函数,得到了这类保形拟插值函数在具有线性再生性质,并保持原有数据点列的单调性和凸性时分别应满足的条件,并给出几个应用实例.     

构造三角样条小波的一种新方法

首先给出了三角样条函数及其性质,然后在此基础上给出了一种构造三角样条小波的新方法.该方法简单易行,而且构造出的小波具有许多良好的性质,如对称性(具有线性相位或广义线性相位)、良好的时频局部特性、短支集及半正交性等,这些对信号处理是非常重要的.     

多小波与多进小波滤波器研究

本文给出了多小波与多进小波的滤波器构造过程,得到了它们的一些良好性质,并给了具体的实例,最后还对某些类型的多小波滤波器、多进小波滤波器之间存在的关系作了研究.     

具有重结点的B-样条曲面G1的连续条件

本文得到了关于两个双三次内部重结点B-样条曲面片G1连续的充分必要条件和在公共边界线上控制向量的本征条件.这些条件直接由两个B-样条曲面的控制向量表示.文[10]证明了使用内部单结点的双三次B-样条曲面来构造G1光滑曲面,局部格式不存在.使用本文的这些条件就可以构造出具有局部各式的G1光滑造型.     

基于众数回归的变系数部分非线性模型的稳健估计

针对变系数部分非线性模型,提出了一种稳健的基于众数回归的两阶段估计方法.首先,基于B-样条函数近似系数函数,利用QR正交分解技术构造了非线性模型,得到了参数的非线性最小二乘估计.其次,提出了变系数函数的众数回归估计量.在一定条件下,证明了估计量的渐近性质.通过数值模拟和实际数据分析,说明了所提估计方法的有效性.     

最优多进Haar小波及在图像压缩中的应用

我们提出了最优多进Haar小波的概念,证明了其存在性和唯一性,给出了最优多进Haar小波构造的通用方法,并证明了最优多进Haar小波具有线性相位,在消失矩意义下,我们所得到的最优多进Haar小波优于离散余弦变换.同时,我们用图像缩编码的方法验证了最优多进Haar小波的性能优于离散余弦变换的,新的变换可以化为精确的小整数运算,能非常廉价地用集成电路实现,该变换的实用意义在于给图像和视频压缩提供了一个更好的选择.     

适应于图像压缩的11/9小波基构造

根据正交多分辨分析理论,利用求解低通和高通滤波的系数,可构造出多种正交小波.但正交小波中只有Haar小波满足对称性,这不适合在图像处理方面的应用.在提升格式的小波变换出现之前,小波分解通过Mallat算法来完成,而提升格式的小波有显著的优点,运算量少,不同小波运算量减少程度不一样,一般减少在25%到50%之间.文章根据双正交对称紧支集小波的消失矩、对称性、短支撑等一系列条件和其他构造原理,构造出一个适应图像压缩的11/9双正交提升小波,并满足Cohen-Daubechies准则.同时,为了便于小波变换的硬件实现,最佳的状态是,分解和重构滤波系数为二进制分数,且根据不同参数取值,让子带编码增益G_(SBC)达到最大.     

Biorthogonal M-band filter construction using the lifting scheme

The lifting scheme has been proposed as a new idea for the construction of 2-band compactly supported wavelets with compactly-supported duals. The basic idea behind the lifting scheme is that it provides a simple relationship between all multiresolution analyses sharing the same scaling function. It is therefore possible to obtain custom-designed compactly supported wavelets with required regularity, vanishing moments, shape, etc. In this work, we generalize the lifting scheme for the construction of compactly-supported biorthogonal M-band filters. As in the previous case, we used the flexibility of the scheme to exploit the degree of freedom left after satisfying the perfect-reconstruction conditions in order to obtain finite filters with some interesting properties, such as vanishing moments, symmetry, shape, etc., or that satisfy certain optimality requests required for particular applications. Moreover, for these lifted biorthogonal M-band filters, we give an analysis-synthesis algorithm which is more efficient than the standard algorithm realized with filters with similar compression capabilities. This revised version was published online in June 2006 with corrections to the Cover Date.     

Construction of Biorthogonal Discrete Wavelet Transforms Using Interpolatory Splines

We present a new family of biorthogonal wavelet and wavelet packet transforms for discrete periodic signals and a related library of biorthogonal periodic symmetric waveforms. The construction is based on the superconvergence property of the interpolatory polynomial splines of even degrees. The construction of the transforms is performed in a “lifting” manner that allows more efficient implementation and provides tools for custom design of the filters and wavelets. As is common in lifting schemes, the computations can be carried out “in place” and the inverse transform is performed in a reverse order. The difference with the conventional lifting scheme is that all the transforms are implemented in the frequency domain with the use of the fast Fourier transform. Our algorithm allows a stable construction of filters with many vanishing moments. The computational complexity of the algorithm is comparable with the complexity of the standard wavelet transform. Our scheme is based on interpolation and, as such, it involves only samples of signals and it does not require any use of quadrature formulas. In addition, these filters yield perfect frequency resolution.     

Construction of multivariate biorthogonal wavelets with arbitrary vanishing moments

We present a concrete method to build discrete biorthogonal systems such that the wavelet filters have any number of vanishing moments. Several algorithms are proposed to construct multivariate biorthogonal wavelets with any general dilation matrix and arbitrary order of vanishing moments. Examples are provided to illustrate the general theory and the advantages of the algorithms. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Method for the Construction of Families of Biorthogonal Filters with Prescribed Properties

Some necessary and sufficient conditions are given in order to obtain biorthogonal wavelet filters with properties which are usually required in applications, such as symmetry and regularity order, by appropriately choosing the parameters in the lifting scheme. A special class of filters extending the biorthogonal B-spline filters is then proposed and analyzed.     

一个二进小波变换像空间的再生核函数

1 引言小波分析是结合泛函分析、应用数学、逼近论、调和分析、广义函数论等数学知识的结晶,具有深刻的理论意义和广泛的应用范围,被称为"数学显微镜".基于其多分辨分析的特点以及在时、频两域都具有表征信号局部特征的功能,应用它可以解决许多Fourier变换不能解决的难题,为工程应用提供了一种新的、更有效的分析工具[1].     

关于小波正则性的几个问题

本文给出了确定尺度函数正则指数的一个公式,证明了正交的四系数滤波中Daubechies小波正则性最优,并结合B-样条对应的双正交滤波,应用提升格式,增加对偶小波的正则性.     

Pairs of Dual Wavelet Frames from Any Two Refinable Functions

Starting from any two compactly supported refinable functions in L₂(R) with dilation factor d,we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L₂(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest possible. In particular, when we consider symmetric refinable functions, the constructed dual wavelets are also symmetric or antisymmetric. As a consequence, for any compactly supported refinable function in L₂(R), it is possible to construct, explicitly and easily, wavelets that are finite linear combinations of translates (d · – k), and that generate a wavelet frame with an arbitrarily preassigned number of vanishing moments.We illustrate the general theory by examples of such pairs of dual wavelet frames derived from B-spline functions.     

Parameterizations of univariate wavelet tight frames with short support

We give a sufficient condition for the filters to generate wavelet tight frames with compact support, and present the parameterizations of the filters with length from four to eight, which include spline filters and other symmetric filters. Examples of symmetric wavelet tight frames which have the maximum vanishing moments are shown.     

具有一定消失矩的优化线性相位滤波器

利用消失矩特性和编码误差最小,给出了一类有限长线性相位的双正交小波滤波器组BNVF的构造方法,BNVF的综合低通和分解高通的系数为二进分数,将其用于图像的分解与重构时,可避免一些乘法运算．三组BNVF用于图像变换编码时,其压缩性能不亚于Cohen,Daubechies等构造的9／7步滤波器组CDF-9／7,且计算复杂度更低．