用于图象压缩的子波变换的算法结构

在图象信号的传输过程中，为了降低比特率，必须进行图象压缩。数字图象压缩中的一种重要技术是子带编码。子波变换由于其在空间频率的良好局部化性能，特别适合于子带编码。本文从一有限长子波变换的算法结构出发，利用矩阵Ｋｒｏｎｅｃｋｅｒ积的性质提出了一种用于图象压缩的二维有限长离散子波变换的算法结构，并且给出了设计快速子波变换算法的方法。     

基于最佳补偿比例因子的整数小波变换

为了提高提升格式下整数小波变换的有损压缩性能,提出了基于最佳补偿比例因子的优化算法。根据变换后小波系数和滤波器的特性,分别采用子带近似线性逼近和量化补偿噪声取代取整运算的方法,求得小波分解后各个子带的最佳补偿比例因子。利用这个比例因子补偿整数小波变换的非线性带来的近似误差以达到优化目的。实验结果表明,在不增加运算复杂度的情况下,所得压缩图像的峰值信噪比(PSNR)与基于浮点运算的传统离散小波变换几乎一样。     

Pattern recognition in multilinear space and its applications: mathematics,computational algorithms and numerical validations

We clarify the mathematical equivalence between low-dimensional singular value decomposition and low-order tensor principal component analysis for two- and three-dimensional images. Furthermore, we show that the two- and three-dimensional discrete cosine transforms are, respectively, acceptable approximations to two- and three-dimensional singular value decomposition and classical principal component analysis. Moreover, for the practical computation in two-dimensional singular value decomposition, we introduce the marginal eigenvector method, which was proposed for image compression. For three-dimensional singular value decomposition, we also show an iterative algorithm. To evaluate the performances of the marginal eigenvector method and two-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for six datasets of two-dimensional image patterns. To evaluate the performances of the iterative algorithm and three-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for datasets of gait patterns and human organs. For two- and three-dimensional images, the two- and three-dimensional discrete cosine transforms give almost the same recognition rates as the marginal eigenvector method and iterative algorithm, respectively.     

量子Haar小波变换算法设计及应用

设计了基于通用量子语言Q_language的量子Haar小波变换算法,该算法对于小波变换的应用和量子算法的完善具有重要的意义.分析了3个量子位Haar小波变换过程,给出了量子Haar小波变换算法的Q_language语言描述,并分析得出其时间和空间复杂度,然后给出了实现量子Haar小渡变换应用方法.     

Nonlinear Discrete Wavelet Transforms over Finite Sets and an Application to Binary Image Compression

The discrete wavelet transform was originally a linear operator that works on signals that are modeled as functions from the integers into the real or complex numbers. However, many signals have discrete function values. This paper builds on two recent developments: the extension of the discrete wavelet transform to finite-valued signals and the research of nonlinear wavelet transforms triggered by the introduction of the lifting scheme by Sweldens. It defines discrete wavelet transforms as bijective, translation-invariant decompositions of signals that are functions from the integers into any finite set. Such transforms are essentially nonlinear, but they can be calculated very time efficiently since only discrete arithmetic is needed. Properties of these generalized discrete wavelet transforms are given along with an elaborate example of such a transform. In addition, the paper presents some ideas to find explicit examples of discrete wavelet transforms over finite sets. These ideas are used to show that, in case the finite set is a ring, there are much more nonlinear transforms than linear transforms. Finally, the paper exploits this increased number of transforms to do lossless compression of binary images.The research is sponsored (grant no. 613.006.570) by the Dutch Science Foundation (NWO).     

量子Daubechies-D（4）小波变换算法及应用研究

由于量子计算相比经典计算具有突出的优越性,设计基于通用量子语言Q_language的量子Daubechies-D（4）小波变换算法对于小波变换的应用和量子算法的完善具有重要的意义。文章分析了Daubechies-D（4）小波变换过程,给出了量子Daubechies-D（4）小波变换算法的Q_language语言描述,并分析得出其时间和空间复杂度,给出了实现量子Daubechies-D（4）小波变换应用方法。     

Fractional dual tree complex wavelet transform and its application to biometric security during communication and transmission

In this paper, the dual tree complex wavelet transform, which is an important tool and recent advancement in signal and image processing, has been generalized by coalescing dual tree complex wavelet transform and fractional Fourier transform. The new transform, i.e. the fractional dual tree complex wavelet transform (FrDT-CWT) inherits the excellent mathematical properties of dual tree complex wavelet transform and fractional Fourier transform. Possible applications of the proposed transform are in biometrics, image compression, image transmission, transient signal processing etc. In this paper, biometric is chosen as the primary application and hence a new technique is proposed for securing biometrics during communication and transmission over insecure channel.     

一种新的无损小波图像压缩算法

基于Daubechies 5-3旋转小波，本文提出了一种无损图像压缩新算法，这一工作证实了小波压缩的如下问题，小波压缩具有与JPEG那样快的运行速度，在不改变变换系数的条件下，采用序贯处理方法能急剧地减小存储器的需要量，能用小波实现图像的无损压缩，对比实验表明，这种快速，有效的无损图像压缩技术比标准的JBIG和无损的JPEG性能要优越。     

索引算法及其在图像多尺度变换中的应用

给出了几种索引算法模型,然后分析了整数提升小波变换的性质,针对其索引算法的索引矩阵存储空间问题,对5/3小波变换进行改造,提出了一个新的图像多尺度变换,该变换后得到高频系数和低频系数的动态范围与原始图像像素值的动态范围相同,从而可实现多级可逆索引算法。实验结果显示,基于索引算法的图像多尺度变换的速度较普通方法有显著提高。     

基于小波与复倒谱变换的音频数字水印算法

为提高水印安全性,提出一种基于小波分解和复倒谱变换的音频数字水印算法。通过对原始语音信号进行三级小波分解,提取小波近似分量,对小波近似分量进行复倒谱变换。实验结果证明,该算法具有较强不可感知性和鲁棒性,能经受添加噪声、低通滤波、重采样、有损压缩等常见信号攻击。     

基于整数小波变换的图像无损压缩方法

本文提出了一种基于整数的第二代小波变换图像无损压缩算法,它克服了第一代小波变换所存在的缺陷。首先将图像进行整数小波变换,然后利用不同子带的小波系数分布特性,对不同的子带采用不同的预测方式,对预测误差进行哈夫曼编码。与JPEG无损压缩模式相比较,该算法方法简单,有较好的压缩性能。     

改进的嵌入式小波在航天图像压缩上的应用

JPEG2000是基于小波变换的图像压缩技术,它不像传统的压缩技术,JPEG2000的良好的压缩效果取决于选取好的小波.嵌入式零树小波编码算法是基于小波变换的一种图像压缩方法,也是有相对不错的压缩效果。对此研究将以嵌入式零树小波为基础,改进其算法,实现在航天项目上的快速高效的压缩图像。     

(9,7)小波变换的MMX实现方法

在图像压缩算法中，人们经常采用小波变换方法对图像数据进行变换处理，（9，7）小波是经常采用的，由于（9，7）小波运算是浮点运算，用传统的C语言编程来运行（9，7）小波变换，运算速度是不能令人满意的，为了尽可能块的实现小波变换，文中提出用MMX技术将浮点数变成整数运算为实现小波变换的实现方法，它比C语言实现速度快很多。     

Image Data Compression using Zonal Sampling and Piecewise-Linear Transforms

In this paper, image data compression methods based on sample selection in the piecewise-linear transform domain will be presented. The image is subjected to a 2-dimensional piecewise-linear transformation and some coefficients will be selected using threshold method and a proposed zonal sampling method. In the proposed zonal sampling method all samples outside the selected zone will be discarded completely (no zeros are replaced). The inverse transformation in this case will have a dimension equal to that of the selected zone. Thus the number of computations needed for the inverse transformation is reduced. The Peak Signal-to-Noise Ratio (PSNR) is used as a measure of quality of the reconstructed images. Comparisons of the compression ability using piecewise-linear transforms and some selected orthogonal transforms such as Walsh and cosine transforms are given. The results obtained by using the proposed zonal sampling method show that the piecewise-linear transforms have a better performance than the orthogonal transforms.     

传感器网络中分布式最优小波压缩算法

研究传感器网络中的小波变换问题,提出了一种基于最优小波变换的分布式数据压缩算法。主要工作有：（1）提出基于混合分解的分布式小波变换,利用节点的计算能力减少节点间交换数据产生小波系数的通信开销;（2）提出自适应小波变换,最优变换级根据小波变换的压缩增益和由此产生的网络开销自适应确定。仿真实验表明,和现有的小波数据压缩算法以及非分布式方式相比,提出的算法具有更优的网络性能。     

多量子位量子小波变换逻辑线路及仿真实现

由于量子计算相比于经典计算的突出优越性,量子小波变换的实现对于小波变换的理论完善和实际应用具有重要的意义,而逻辑线路是该变换实现的基础。应用多量子算符代数理论设计了3量子位Haar和D^（4）小波变换的逻辑线路,进而将逻辑线路转化成核磁共振系统可以实现的脉冲序列,并在量子计算仿真器（QCE）上进行了模拟实现,验证了逻辑线路的合理性。     

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。     

矢量积小波变换

1 矢量小波函数方程Ψ(x)=sum from k=0 to N(C_kΨ(2x-k)) (1)称为尺度方程,它在多尺度分析中起着举足轻重的作用。方程(1)的系数可以是实数亦可以是复数,(1)式的解Ψ(x)称为尺度函数。若式(1)有一个可积解Ψ(x),且是L~2(R)中的一个规范正交基,则从下式Ψ(x)=sum from k=0 to N(-1)~k(C_(N-k)Ψ(2x-k)) (2)     

一种改进的无线多媒体传感器网络分布式图像压缩算法

针对无线多媒体传感器网络(WMSNs)中单个节点资源严重受限而难以直接处理和传输图像的问题,在分布式渐进图像压缩算法(DICA)的基础上,提出了一种改进的基于簇内分布式处理的图像压缩算法(ICDP),即在每个簇内通过能量优先选择原则选取辅助节点来协同完成JPEG2000图像压缩标准中的多级小波变换,从而实现图像的分布式处理和压缩。仿真结果表明,与DICA算法相比,ICDP算法能够在保证图像重建质量和压缩比相同的前提下,更好地平衡网络中各节点能耗,延长了网络的生命周期,更适合应用于资源受限、节点部署密集的WMSNs中。     

基于小波变换的非渐进网格压缩

为了取得较好的三角形网格压缩性能，提出了一种基于小波变换的三角形网格非渐进压缩方法。该压缩方法先利用重新网格化来去除大部分连接信息，然后利用小波变换的强去相关能力来压缩几何信息。在进行重新网格化和小波变换后，再按一个确定的次序将所有的小波系数扫描为一个序列，然后对其做量化和算术编码。另外，对重新网格化得到的自适应半正规采样模式，还设计了一种自适应细分信息编码算法，以便使解码端知道每一个小波系数应该放置在哪一个顶点上。实验表明，用该压缩方法对由三维扫描仪获取的复杂网格进行压缩，取得了比Edgebreaker方法明显要好的率失真性能；10比特量化时，压缩倍数在200倍左右，为Edgebreaker方法的2倍多。