离散Arnold变换改进及其在图像置乱加密中的应用

为了改善传统二维Arnold变换用于图像置乱加密的效果,提出了离散Arnold变换的改进方法,并将其用于图像置乱加密测试研究.该方法利用现有离散标准映射的构造思想,将传统离散二维Arnold变换表达式中第一个变换表达式所对应变换结果非线性融入第二个变换表达式,实现经典离散二维Arnold变换的非线性去拟仿射化修改,以便快速改善图像置乱加密效果.数学证明改进方法不再保持现有离散二维Arnold变换所具有的拟仿射不变性,但是改进变换仍是一种具有周期性的可逆映射,将其用于图像置乱加密时,利用其周期性或逆变换能恢复置乱前原图像.大量实验结果表明,本文所建议的改进方法是有效的,相比现有的离散Arnold变换更具有实用价值意义.     

基于提升方案的CDF(1,5)整-整可逆双正交小波变换在渐进性无损图像压缩中的应用

讨论了基于双正交小波变换提升方案在图像压缩中的应用 ,研究了CDF( 1,3) ,CDF( 1,5 )双正交小波消失矩对图像压缩的影响。实验结果表明 ,在图像压缩中应尽可能选取具有较高消失矩的双正交小波 ,用CDF( 1,5 )双正交小波提升方案实现了基于整数运算的整 整可逆双正交小波变换 ,以及快速的、渐进性的直至无损图像压缩     

基于高速公路裂纹局部线性特征内容的脊波变换域算法研究

利用频域中傅里叶变换投影定理,提出一种新的离散脊波实现算法,应用于高速公路局部线性裂纹的检测取得较好效果。详细阐述了离散脊波的实现步骤以及对标准图像进行脊波变换的模拟结果,并提出拉东(Radon)变换重建原图像的基本条件。上述定理应用于复杂背景下的路面检测,结合直方图均衡化算法消除背景噪声;选用基于样本估计的阈值方法对脊波分解的各层系数进行处理去除随机噪声。选用不同的重构系数进行计算,得到脊波变换后重构图像的信噪比优于二维小波变换(低频大于20dB)以及二维小波变换加魏纳滤波变换(平均大于3dB)。通过图像的二值化处理提取局部线性裂纹,其分辨力极限达到2mm精度。     

基于SPIHT的图像加密与压缩关联算法

为了研究图像压缩与加密同步进行问题, 本文提出了一种在变换域下的图像加密与压缩关联算法在该算法中, 加密过程发生在小波变换与SPIHT编码之间它充分利用了离散小波变换和基于层次树的集合划分(set partitioning in hierarchical trees, SPIHT)编码属性, 扩散过程被限制在单个子带内部. 此外, 混淆过程保留了SPIHT编码中两个最重要的位和符号位, 它包含了图像的重要信息. 实验结果表明, 算法具有良好的安全性、图像重构视觉质量以及很高的加/解密速度.     

二维提升的CDF(1,3)小波结合改进的SPIHT的渐进性无损图像压缩方法

针对传统小波变换计算复杂的缺点和多级树集合分裂算法(SPIHT)编码过程重复运算、存储量大的问题,提出了一种二维提升的CDF(1,3)小波结合改进的SPIHT的渐进性无损图像压缩方法。对整数CDF(1,3)双正交小波变换实现二维提升,利用提升的小波对图像做变换,提高了运算速度、便于硬件实现。对SPIHT算法加以改进,根据各个子图像的不同特点,改变扫描路线,采用四路并行分块处理的方法,提高了编码速度,降低了编解码过程的运算复杂度和时间消耗。利用提升的CDF(1,3)小波变换结合改进的SPIHT实现了渐进性无损图像压缩,证明了二维提升方案的有效性。     

基于整型可逆时域交叠变换的遥感图像压缩

提出了一种无乘法整型可逆时域交叠变换方法,并以此为核心变换技术设计了一种新的有损到无损渐进的图像压缩系统.利用所提出的压缩系统从一个单一的码流文件中既可以恢复出完全无损的图像,也可以在高压缩比下得到高质量的有损重构图像.算法通过前后向滤波器改进离散余弦变换性能,并在矩阵分解基础上通过多阶提升实现完全可逆整型变换.光学遥感图像的实验结果显示,该算法在绝大多数情况下可以达到优于图像压缩国际标准JPEGJ、PEG2000以及新一代压缩算法HD-Photo的率失真性能以及高质量的主观视觉效果.     

基于整型可逆时域交叠变换的遥感图像压缩

提出了一种无乘法整型可逆时域交叠变换方法,并以此为核心变换技术设计了一种新的有损到无损渐进的图像压缩系统.利用所提出的压缩系统从一个单一的码流文件中既可以恢复出完全无损的图像,也可以在高压缩比下得到高质量的有损重构图像.算法通过前后向滤波器改进离散余弦变换性能,并在矩阵分解基础上通过多阶提升实现完全可逆整型变换.光学遥感图像的实验结果显示,该算法在绝大多数情况下可以达到优于图像压缩国际标准JPEG、JPEG2000以及新一代压缩算法HD-Photo的率失真性能以及高质量的主观视觉效果.     

基于结构光投影的二维S变换轮廓术

S变换是一种集合了窗口傅里叶变换和小波变换优点的时频分析技术,目前一维S变换已成功应用于结构光投影的条纹相位解调中。由于二维S变换可以对图像在两个方向上进行时频分析,具有更优于一维S变换的分析和处理能力。为了完善S变换的条纹相位解调理论,将二维S变换方法引入到基于结构光投影的三维光学测量中,研究了二维S变换在条纹相位解调中的原理及应用,给出了详尽的理论分析,并同一维S变换结果进行了比较。模拟和实验都表明,在条纹图解相中,二维S变换比一维S变换提取的相位精度更高,即使在存在较严重噪声污染的情况下也表现出良好的可靠性,体现出二维S变换提取相位的优势。     

一种基于压缩感知的三维导体目标电磁散射问题的快速求解方法

提出了一种将压缩感知和特征基函数结合的方法来计算三维导体目标的雷达散射截面.利用压缩感知理论,将随机选择的矩量法阻抗矩阵作为测量矩阵,将激励电压视为测量值,然后再用恢复算法可实现二维或二维半目标感应电流的求解.对于三维导体目标,使用Rao-Wilton-Glisson基函数表示的感应电流在常用的离散余弦变换基、小波基等稀疏基上不稀疏.为此,本文将计算出的目标特征基函数作为稀疏基,用广义正交匹配追踪算法作为恢复算法来加速恢复过程,并应用到三维导体目标的雷达散射截面计算中.数值结果证明了本文方法的准确性与高效性.     

Cosh-Hilbert变换反演的矩方法及其在单光子发射计算机断层成像中的应用

基于反演Hilbert变换的Tricomi公式和双曲余弦函数Taylor展开,给出一种反演双曲余弦Hilbert变换(CHT)的数值算法,并应用于单光子发射计算机断层成像.利用Taylor展开将函数的CHT变换表示为其Hilbert变换和由各阶矩组成的修正项.利用Tricomi公式得到一个关于函数各阶矩的线性方程组.通过对方程组的截断,可以求得函数的有限阶矩,并得到函数的近似重建.通过数值实验与精确重建公式进行比较,验证了算法的有效性.     

二维轴对称图象高阶胡氏不变矩快速算法的改进

提出了基于二维轴对称性目标图象矩快速算法的实用化改进方案.算法实用化改进是通过两个命题的证明实现的.一是通过轴对称目标图象质心在对称轴上的命题证明,实现了将二维轴对称图象矩快速算法用于轴对称性图象中心矩的计算;二是通过目标图象以坐标系中任意两点为圆心,旋转相同角度,结果图象具有平移性的命题证明,实现了算法用于对旋转不同角度的对称目标图象的中心矩的计算改进.在此基础上,完成了二维轴对称目标图象高阶胡氏不变矩实用化快速算法的实现.实验证明,该算法具有较好的实时性能,且具有较小的引入误差.     

Conditional quadrature method of moments for kinetic equations

Kinetic equations arise in a wide variety of physical systems and efficient numerical methods are needed for their solution. Moment methods are an important class of approximate models derived from kinetic equations, but require closure to truncate the moment set. In quadrature-based moment methods (QBMM), closure is achieved by inverting a finite set of moments to reconstruct a point distribution from which all unclosed moments (e.g. spatial fluxes) can be related to the finite moment set. In this work, a novel moment-inversion algorithm, based on 1-D adaptive quadrature of conditional velocity moments, is introduced and shown to always yield realizable distribution functions (i.e. non-negative quadrature weights). This conditional quadrature method of moments (CQMOM) can be used to compute exact N-point quadratures for multi-valued solutions (also known as the multi-variate truncated moment problem), and provides optimal approximations of continuous distributions. In order to control numerical errors arising in volume averaging and spatial transport, an adaptive 1-D quadrature algorithm is formulated for use with CQMOM. The use of adaptive CQMOM in the context of QBMM for the solution of kinetic equations is illustrated by applying it to problems involving particle trajectory crossing (i.e. collision-less systems), elastic and inelastic particle–particle collisions, and external forces (i.e. fluid drag).     

用多消失矩最优小波包基改进虹膜识别

采用层叠算法求出尺度函数和小波函数的离散采样序列的逼进，将不具有基函数解析表达式的母小波用于虹膜特征提取，并利于实现连续小波包变换.针对虹膜光学识别应用背景，提出采用基于连续小波包变换的多消失矩联合最优小波包基来改进特征图像相关识别的最优基，并用统计识别方法进行后处理以增强算法适应性，同时提出通过体全息相关系统来实现，以发挥光学高并行性的优势，模拟结果表明可获得比已有方法更高的识别率.     

基于蚁群算法的二维最大熵分割算法

由于二维最大熵分割法不仅考虑了像素的灰度信息,而且还充分利用了像素的空间邻域信息,因此能够取得较好的分割效果.但是,该方法的计算量巨大,不利于红外图像的快速处理.蚁群算法于20世纪90年代初提出,是受到蚁群集体行为的启发而提出的一种基于种群的模拟进化算法,属于随机搜索算法.该算法已经成功应用于旅行商等离散问题.将蚁群算法应用于二维最大熵法,提出了基于蚁群算法的二维最大熵分割算法.与传统的穷尽搜索法相比,求解速度提高了60倍左右.仿真实验表明,该方法快速、简单、有效.     

Numerical Algorithms for Estimating Probability Density Function Based on the Maximum Entropy Principle and Fup Basis Functions

Estimation of the probability density function from the statistical power moments presents a challenging nonlinear numerical problem posed by unbalanced nonlinearities, numerical instability and a lack of convergence, especially for larger numbers of moments. Despite many numerical improvements over the past two decades, the classical moment problem of maximum entropy (MaxEnt) is still a very demanding numerical and statistical task. Among others, it was presented how Fup basis functions with compact support can significantly improve the convergence properties of the mentioned nonlinear algorithm, but still, there is a lot of obstacles to an efficient pdf solution in different applied examples. Therefore, besides the mentioned classical nonlinear Algorithm 1, in this paper, we present a linear approximation of the MaxEnt moment problem as Algorithm 2 using exponential Fup basis functions. Algorithm 2 solves the linear problem, satisfying only the proposed moments, using an optimal exponential tension parameter that maximizes Shannon entropy. Algorithm 2 is very efficient for larger numbers of moments and especially for skewed pdfs. Since both Algorithms have pros and cons, a hybrid strategy is proposed to combine their best approximation properties.     

Evaluation of the Fast Inverse Laplace Transform for Three-Dimensional NMR Distribution Functions

A fast inverse Laplace transform (ILT) for the three-dimensional (3-D) nuclear magnetic resonance distribution was proposed by the authors with a designed pulse sequence and an efficient data-processing algorithm in Zhang et al. (Appl Magn Reson 44:849–857, 2013). In this paper, evaluation method to the 3-D ILT algorithm is introduced and the simulation results using simulated data with three different signal-to-noise ratios demonstrate that the precision and speed are excellent.     

On Solving Three-Dimensional Electrostatic Field Distribution by Multigrid Method

A highly efficient numerical algorithm using the multigrid method (MGM) is introduced to solve a three-dimensional (3-D)field distribution. Taking advantage of the restriction and prolongation in MGM computation, a more accurate field distribution can be acquired rapidly. According to the MGM algorithm, a 3-D program is accomplished, which can solve the field distributions in electron optical systems for various electrostatic lenses. The 3-D field distribution in an electrostatic concentric spherical model is tested with the MGM algorithm and with an algorithm based on the finite difference method (FDM). Comparing these two results in terms of computational efficiency and computational accuracy, it appears that MGM is superior to FDM, which is now used the most in field computations. This paper shows that the 3-D field computation using MGM greatly improves the computational efficiency of field distributions in electron optical systems and shortens the computational time.     

On the unstable discrete spectrum of the linearized 2-D Euler equations in bounded domains

We investigate the behavior of the unstable discrete spectrum of the linearized 2-D Euler equation when the domain is smoothly perturbed. It is shown that when a self-adjoint Schrödinger-type operator undergoes a codimension-1 bifurcation it translates into a bifurcation in the linearized Euler equation associated with an instability either appearing or disappearing.We give sufficient conditions in order to observe smooth quadratic growth of the unstable eigencurves of the linearized Euler equation. The critical exponent is explicitly given as a function of the null-vector involved into the codimension-1 bifurcation using first and second-order moments of a Laplace transform.This analysis provides an explanation for the successive symmetry-breaking bifurcations observed in models of the mid-latitude oceans. An explicit example is also given.     

一种基于DFT时域插值的OFDM水声信道估计改进方法

信道估计作为OFDM通信系统中的重要部分,其性能关系到整个系统的误比特率。本文提出了一种基于DFT时域插值的信道估计改进方法,用于OFDM水声通信系统。该方法利用噪声门限抑制多径之间的信道估计噪声,计算简单,达到较好的信道估计效果。对该方法进行了理论分析,仿真实验以及海试。在海试中得到传输距离2km,有效数据率2.8kbit/s,证明该方法可以用于中短程浅海水声通信。