基于小波边缘刻画与LBF水平集变分模型的图像分割

本文研究了基于水平集的图像分割的问题.利用小波变换的方法,构造出图像边缘刻画函数,引入到LBF水平集分割变分模型中,获得了基于小波变换的WLBF模型,同时给出了WLBF模型的数值求解算法.针对不同情景下的典型灰度图像,给出了图像分割实例,推广了LBF模型及算法,实验结果证明WLBF模型及算法对图像分割的有效性.     

基于小波变换的Laws纹理测度在植被分割中的应用

针对从全色航空影像中进行植被区域提取的随机性和复杂性,阐述了一种基于小波的Laws纹理测度进行植被提取的新算法,它的特点是先用小波变换将图像变换到不同的尺度层上,然后再在多尺度层上提取Laws纹理测度,形成植被区域的特征.与传统的植被提取方法比,它用到了不同频率上纹理的Laws信息,从而更准确的刻画了植被区域的纹理特征,试验结果表明:基于小波变换的Laws纹理测度对植被有较好的分割效果.     

多小波图像插值算法研究

与单小波变换一样,多小波变换同样具有多分辨分析的特性,1次多小波变换可以将图像分解成4个低频子带和12个高频子带,而且原图像的大小是每个子带的4倍.根据多小波变换的这一特点,利用原图像与经过1次多小波变换后的各高频子带的信息,并考虑各子带的分形维数,提出了一种新颖的灰度图像插值算法.实验结果表明,与传统的插值算法相比,例如双线性插值与双三次多项式插值,该算法的插值效果较好,且克服了单小波插值中出现的斑点干扰.     

基于小波去噪和梯度校正的分水岭图像分割技术研究

本文研究了基于分水岭方法的图像分割问题.利用最大熵算法,对梯度图像进行校正.数值实验结果表明,本文提出的分割算法获得了良好的图像分割效果.     

测地线活动轮廓模型的图像分割快速算法

从最优化理论的角度来看,目前求解图像分割的测地线活动轮廓(geodesic active contour,GAC)模型大多采用固定步长的最速下降算法.而众所周知,该算法收敛速度较慢,这在能量泛函的梯度较小时尤为明显.对求解GAC模型的快速算法进行了研究.首先,回顾了GAC模型的演化方程;随后,将共轭梯度(conjugate gradient,CG)算法引入到GAC模型的求解中,形成一种新的求解图像分割问题的数值方法,即GAC模型的CG算法;最后,通过试验对比传统的数值方法,表明CG算法具有良好的收敛性.     

基于小波域的多尺度非参数图像分割方法

主要介绍了一种基于信息熵理论及图像多尺度信息来对图像进行非参数主动轮廓模型分割的有效方法.由于小波多分辨率特性的引入,可以最大程度地利用图像多尺度信息以确保分割的准确性和完整性.又由于小波变换的特性,低频信息的使用更是进一步降低了噪声影响.文中把图像分割问题定义为在分割区域边缘长度满足一定约束条件下,图像标记场与各个尺度图像像素值之间的互信息熵最大化过程.该方法可以有效地降低噪声对于分割的影响,及确保分割的准确性和完整性.     

基于自适应小波变换和矢量量化的图像压缩编码

运用小波变换进行图像压缩的算法其核心都是小波变换的多分辨率分析以及对不同尺度的小波系数的量化和编码 .本文提出了一种基于能量的自适应小波变换和矢量量化相结合的压缩算法 .即在一定的能量准则下 ,根据子图像的能量大小决定是否进行小波分解 ,然后给出恰当的小波系数量化 .在量化过程中 ,采用一种改进的LBG算法进行码书的训练 .实验表明 ,本算法广泛适用于不同特征的数字图像 ,在取得较高峰值信噪比的同时可以获得较高的重建图像质量 .     

基于混合细菌趋药性的聚类分割算法

为解决模糊C均值算法对初始值敏感、容易陷入局部极值的问题,提出基于混合细菌趋药性的聚类分割算法,在简单细菌趋药性算法的基础上,将粒子群算法引入.新算法使用粒子群算法、细菌趋药性算法两步优化得到的结果作为模糊C均值算法的初始值,同时新算法中引入精英保持策略,进一步提高算法效率.实验结果表明,新算法具有较快的收敛速度,.同时能够获得较好的图像分割效果和质量.     

车牌识别机器学习方法的数学建模与实现

首先,针对不同光照、复杂背景和投影失真的车牌图像建立基于Adaboost算法和改进Haar特征的车牌检测模型;然后,运用Radon变换进行车牌校正,并结合3次B样条小波变换和识别反馈模型对字符进行粗和精分割;最后,根据汉字和数字字母的不同结构特征,采用不同的算法提取特征,特别是针对车牌字符特点,训练汉字、字母和数字字母3种神经网络模型用于建立字符识别模型.实验结果表明该模型是实用的.     

基于小波多分辨率分析和改进窄带法的C-V水平集图像分割模型

本文研究了基于小波分析改进的C-V模型图像分割问题.利用小波多分辨率分析和改进的窄带水平集方法,获得了比传统C-V模型分割速度更快、准确度更高、算法复杂度更低的分割结果.推广了C-V水平集模型如何快速准确地分割灰度不均匀的图像和窄带水平集法等结果.     

A penalised data-driven block shrinkage approach to empirical Bayes wavelet estimation

In this paper we propose a simple Bayesian block wavelet shrinkage method for estimating an unknown function in the presence of Gaussian noise. A data-driven procedure which can adaptively choose the block size and the shrinkage level at each resolution level is provided. The asymptotic property of the proposed method, BBN (Bayesian BlockNorm shrinkage), is investigated in the Besov sequence space. The numerical performance and comparisons with some of existing wavelet denoising methods show that the new method can achieve good performance but with the least computational time.     

相关数据密度函数的非线性小波估计

本文考虑了严平稳随机序列密度函数的非线性小波估计,证明了在Besov空间中,非线性小波估计可达到最优收敛速度.进一步讨论了自适应非线性小波估计,证明了自适非线性小波估计可达到次最优速度即和最优速度相差in n.     

Wavelet estimation in diffusions with periodicity

We consider a time-inhomogeneous diffusion process, whose drift term contains a deterministic T-periodic signal with known periodicity. This signal is supposed to be contained in a Besov space, we try to estimate it using a non-parametric wavelet estimator. Our estimator is inspired by the thresholded wavelet density estimator constructed by Donoho, Johnstone, Kerkyacharian and Picard in 1996. Under certain ergodicity assumptions to the process, we can give the same asymptotic rate of convergence as for the density estimator.     

MULTILEVEL AUGMENTATION METHODS FOR SOLVING OPERATOR EQUATIONS

We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstra     

Wavelet linear estimations of density derivatives from a negatively associated stratified size-biased sample

We define a wavelet linear estimator for density derivative in Besov space based on a negatively associated stratified size-biased random sample. We provide two upper bounds of wavelet estimations on L^p （1 ≤ p 〈 ∞） risk.     

Optimal Time Decay of Navier–Stokes Equations with Low Regularity Initial Data

In this paper, we study the optimal time decay rate of isentropic Navier–Stokes equations under the low regularity assumptions about initial data. In the previous works about optimal time decay rate, the initial data need to be small in H~([N/2]+2)(R~N). Our work combined negative Besov space estimates and the conventional energy estimates in Besov space framework which is developed by Danchin. Through our methods, we can get optimal time decay rate with initial data just small in B~(N/2-1,N/2+1)∩B~(N/2-1,N/2) and belong to some negative Besov space(need not to be small). Finally,combining the recent results in [25] with our methods, we only need the initial data to be small in homogeneous Besov spaceB~(N/2-2,N/2)∩B~(N/2-1) to get the optimal time decay rate in space L~2.     

Besov regularity for second order elliptic boundary value problems with variable coefficients

This paper is concerned with some theoretical foundations for adaptive numerical methods for elliptic boundary value problems. The approximation order that can be achieved by such an adaptive method is determined by certain Besov regularity of the weak solution. We study Besov regularity for second order elliptic problems in bounded domains in ℝ ^d . The investigations are based on intermediate Schauder estimates and on some potential theoretic framework. Moreover, we use characterizations of Besov spaces by wavelet expansions. This work has been supported by the Deutsche Forschungsgemeinschaft (Da 360/1-1)     

Multi-parameter Triebel-Lizorkin and Besov spaces associated with flag singular integrals

Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.     

Adaptive Wavelet Methods for Elliptic Operator Equations with Nonlinear Terms

We present an adaptive wavelet method for the numerical solution of elliptic operator equations with nonlinear terms. This method is developed based on tree approximations for the solution of the equations and adaptive fast reconstruction of nonlinear functionals of wavelet expansions. We introduce a constructive greedy scheme for the construction of such tree approximations. Adaptive strategies of both continuous and discrete versions are proposed. We prove that these adaptive methods generate approximate solutions with optimal order in both of convergence and computational complexity when the solutions have certain degree of Besov regularity.     

Local means,wavelet bases and wavelet isomorphisms in Besov‐Morrey and Triebel‐Lizorkin‐Morrey spaces

We consider local means with bounded smoothness for Besov‐Morrey and Triebel‐Lizorkin‐Morrey spaces. Based on those we derive characterizations of these spaces in terms of Daubechies, Meyer, Bernstein (spline) and more general r‐regular (father) wavelets, finally in terms of (biorthogonal) wavelets which can serve as molecules and local means, respectively. Hereby both, local means and wavelet decompositions satisfy natural conditions concerning smoothness and cancellation (moment conditions). Moreover, the given representations by wavelets are unique and yield isomorphisms between the considered function spaces and appropriate sequence spaces of wavelet coefficients. These wavelet representations lead to wavelet bases if, and only if, the function spaces coincide with certain classical Besov‐Triebel‐Lizorkin spaces.