离散小波变换域LMS自适应消噪

本文按照自成体系的离散小波变换正交分解框架,直接从离散域出发,得出离散小波变换域ＬＭＳ（ＤＷＬＭＳ）,变换的正交性与采样率无关,并可使用Ｍａｌｌａｔ快速算法。方法可减小自适应应滤波器输入向量自相关阵的谱动态范围,提出了传统ＬＭＳ算法的收敛速度和稳定性。     

基于多小波的图像压缩

多小波以其具有正交性、对称性、短支撑和较大的消失矩等多个良好特性弥补了单小波的不足.在介绍多小波理论的基础上,提出一种新的图像压缩方法.该方法以CL多小波为基础,结合SPIHT图像压缩算法,对多小波系数进行压缩处理.采用Matlab 6.5进行实验,实验结果表明,经该算法压缩后的图像,其质量优于一般小波变换的传统方法.     

基于TLS的正交小波变换红外图像去噪

提出了一种基于总体最小二乘的正交小波变换红外图像去噪算法。对红外图像进行离散正交小波变换,分别对各个分解层的高频子带,通过总体最小二乘算法估计小波系数,获得各个高频子带信号的估计系数,然后通过正交小波反变换得到去噪图像。仿真结果表明,该红外图像去噪算法能有效去除加性红外图像噪声,在信噪比、直方图匹配等方面都有较大改善,并获得了良好的主观视觉效果。     

基于自适应正交小波基的图像分解

简单介绍了傅利叶变换以及傅立叶加窗变换的局限性，以及小波变换的提出对这一局限性的有效解决。重点介绍了小波变换基本原理，正交小波基的概念，以及正交小波分解回复算法。并用程序实现了正交小波基的统一解析构造方法。最后，利用小波算法对图像的水平和垂直细节进行提取，并给出了分解结果。     

反对称双正交小波应用于多尺度边缘提取的研究

本文对反对称双正交小波所具有的多尺度边缘提取能力进行了理论分析，提出了一种反对称双正交小波变换域内的多尺度边缘提取算法，并通过实验进行了验证。该结果为在基于小波变换的压缩数据域内利用边缘信息实现图像检索提供了依据。     

基于双正交小波域的SAR图像滤波方法

将E-lee、E-Kuan、GammaMap、wiener等经典滤波算法和双正交小波变换相结合,提出了基于双正交小波变换域的局部统计特性SAR图像滤波方法,同时提出了一个运算量少,且是归一化的对数变换,它将乘性的Speckle噪声转为加性噪声。在小波域内建立了局部统计特性SAR图像滤波算法,使用多分辨率的手段,因为在每个方向上的小波系数都具有相同的特征,可以很好地处理图像的一些特性,使得图像边缘被模糊的相对少些。实验结果表明,此方法比经典算法的效果要好。     

基于多小波分解的多光谱图像矢量融合

在实数域中,对称、正交的紧支集非平凡单小波基不存在,而多小波把紧支性、对称性、正交性完美地结合在一起,使小波理论从标量扩展到矢量范畴。考虑到图像多小波变换系数具有矢量特性,该文将基于像素点和基于区域的标量融合策略推广到矢量情形,提出一种新的、在多小波域中基于矢量融合的图像融合算法,充分利用多小波变换域系数矢量内部各个分量的相关性来提高融合质量。两波段真实多光谱图像融合实验结果表明,与单小波标量融合方法相比,多小波矢量融合算法获得的图像具有较优的视觉效果和客观评价指标,从而证明了用于图像融合时,多小波较之单小波更适合于人类视觉系统,具有广泛的应用前景。     

Q-shift复小波的一种新型构造方法及其在图像去噪中的应用

为了提高复小波变换的效率,本文提出了一种设计Q-shift复小波滤波器的新方法。与目前采用多相位矩阵的晶格分解结构得到正交小波的方法不同的是,这里从更为一般的完全重构滤波器组出发寻求满足特定要求的正交小波。不但可以构造出系数更为简单、运算更加方便的小波,而且可以实现任意精度的复小波变换。该方法的可拓展性好,可以很方便的添加如高阶消失矩等限制并简化设计过程。以普遍采用的Q-shift10/10小波为例,利用本文构造的正交小波可将复小波变换中的乘法运算降低到原来的1/3,而加法基本相当,且小波的频率选择性质更好。将其用于图像去噪的实验表明,采用本文构造的小波可以显著提高处理速度并得到更高的峰值信噪比(PSNR)。     

基于小波变换/小波包变换的多载波调制技术

小波/小波包在通信系统中的应用是近年来一个新的研究领域,而基于小波/小波包变换的多载波调制技术是其中一大研究热点。由于小波/小波包基函数具有良好的正交性与时频局域性等特点,基于小波/小波包变换的多载波调制技术,能够有效地提高通信系统性能。本文介绍了当前几种主要的基于小波/小波包变换的多载波调制方案,分析了这些方案的性能特点及发展趋势,并与其他方案进行了比较。     

数字水印中的正交小波基

该文主要研究了水印算法中小波基的选择和正交小波基的性质与水印稳健性的关系。研究结果表明:正交小波基的正则性、消失矩阶数、支撑长度以及小波图像能量在低频带的集中程度对水印稳健性的影响极小。同时也得到了一个有意义的结论:Haar小波比较适合应用于图像水印。该文还研究了在水印算法中,小波变换级数和嵌入公式的选取及其它一些问题。     

一类具有线性相位的二重多小波的构造

给出由实单一紧支撑正交的小波构造二重正交多小波的方法。具体地,首先由实单一的紧支撑尺度函数构造出单一紧支撑正交对称的复尺度函数,再由构造出的复尺度函数去构造二重正交紧支撑多尺度函数,然后给出由二重尺度函数构造二重小波的显式公式。紧支撑正交的单一小波除Haar小波外不具有任何对称性,它用作滤波器不可能有线性相位,而由实单一紧支撑正交的尺度函数构造出的二重尺度函数却是对称的,对应的二重小波可以是对称或反对称的,从而使得这种小波在信号处理的过程中具有线性相位。最后给出相应的构造算例。     

High-order balanced multiwavelets: theory, factorization, anddesign

This paper deals with multiwavelets and the different properties of approximation and smoothness associated with them. In particular, we focus on the important issue of the preservation of discrete-time polynomial signals by multifilterbanks. We introduce and detail the property of balancing for higher degree discrete-time polynomial signals and link it to a very natural factorization of the refinement mask of the lowpass synthesis multifilter. This factorization turns out to be the counterpart for multiwavelets of the well-known zeros at π condition in the usual (scalar) wavelet framework. The property of balancing also proves to be central to the different issues of the preservation of smooth signals by multifilterbanks, the approximation power of finitely generated multiresolution analyses, and the smoothness of the multiscaling functions and multiwavelets. Using these new results, we describe the construction of a family of orthogonal multiwavelets with symmetries and compact support that is indexed by increasing order of balancing. In addition, we also detail, for any given balancing order, the orthogonal multiwavelets with minimum-length multifilters     

Armlets and balanced multiwavelets: flipping filter construction

In the scalar-valued setting, it is well-known that the two-scale sequences {q/sub k/} of Daubechies orthogonal wavelets can be given explicitly by the two-scale sequences {p/sub k/} of their corresponding orthogonal scaling functions, such as q/sub k/=(-1)/sup k/p/sub 1-k/. However, due to the noncommutativity of matrix multiplication, there is little such development in the multiwavelet literature to express the two-scale matrix sequence {Q/sub k/} of an orthogonal multiwavelet in terms of the two-scale matrix sequence {P/sub k/} of its corresponding scaling function vector. This paper, in part, is devoted to this study for the setting of orthogonal multiwavelets of dimension r=2. In particular, the two lowpass filters are flipping filters, whereas the two highpass filters are linear phase. These results will be applied to constructing both a family of the most recently introduced notion of armlet of order n and a family of n-balanced orthogonal multiwavelets.     

Generalized Discrete Multiwavelet Transform With Embedded Orthogonal Symmetric Prefilter Bank

Prefilters are generally applied to the discrete multiwavelet transform (DMWT) for processing scalar signals. To fully utilize the benefit offered by DMWT, it is important to have the prefilter designed appropriately so as to preserve the important properties of multiwavelets. To this end, we have recently shown that it is possible to have the prefilter designed to be maximally decimated, yet preserve the linear phase and orthogonal properties as well as the approximation power of multiwavelets. However, such design requires the point of symmetry of each channel of the prefilter to match with the scaling functions of the target multiwavelet system. It can be very difficult to find a compatible filter bank structure; and in some cases, such filter structure simply does not exist, e.g., for multiwavelets of multiplicity 2. In this paper, we suggest a new DMWT structure in which the prefilter is combined with the first stage of DMWT. The advantage of the new structure is twofold. First, since the prefiltering stage is embedded into DMWT, the computational complexity can be greatly reduced. Experimental results show that an over 20% saving in arithmetic operations can be achieved comparing with the traditional DMWT realizations. Second, the new structure provides additional design freedom that allows the resulting prefilters to be maximally decimated, orthogonal and symmetric even for multiwavelets of low multiplicity. We evaluated the new DMWT structure in terms of computational complexity, energy compaction ratio as well as the compression performance when applying to a VQ based image coding system. Satisfactory results are obtained in all cases comparing with the traditional approaches.     

Orthogonal multiwavelets with optimum time-frequency resolution

A procedure to design orthogonal multiwavelets with good time-frequency resolution is introduced. Formulas to compute the time-durations and the frequency-bandwidths of scaling functions and multiwavelets are obtained. Parameter expressions for the matrix coefficients of the multifilter banks that generate symmetric/antisymmetric scaling functions and multiwavelets supported in [O,N] are presented for N=2,...,6. Orthogonal multiwavelets with optimum time-frequency resolution are constructed, and some optimal multifilter banks are provided     

Fuzzy multiwavelet denoising on ECG signal

Since different multiwavelets, pre- and post-filters, have different impulse and frequency response characteristics, different multiwavelets, preand post-filters, should be selected, integrated and applied at different noise levels if a signal is corrupted by an additive white Gaussian noise (AWGN). Some fuzzy rules on selecting and integrating different multiwavelets, pre- and post-filters together, are proposed. These fuzzy rules are set up based on the training results of the denoising performances of applying different multiwavelets, pre- and post-filters, at different noise levels. When a new electrocardiogram (ECG) signal is applied, the appropriate multiwavelets, pre- and post-filters, are selected and integrated based on fuzzy rules and the noise level of the signal. A hard thresholding is applied on the multiwavelet coefficients. According to an extensive simulation, it was found that the proposed fuzzy rule-based multiwavelet denoising algorithm achieves 30% improvement compared to traditional multiwavelet denoising algorithms.     

GHM类正交多小波滤波器组的因子化和参数化

本文提出了GHM类正交多小波滤波器组的完备的因子化形式和参数化方法。可用于这类多小波的优化设计和有效实现，同时给出了时频最优准则下的设计实例。     

Balanced multiwavelets theory and design

This article deals with multiwavelets, which are a generalization of wavelets in the context of time-varying filter banks and with their applications to signal processing and especially compression. By their inherent structure, multiwavelets are fit for processing multichannel signals. This is the main issue in which we are interested. First, we review material on multiwavelets and their links with multifilter banks and, especially, time-varying filter banks. Then, we have a close look at the problems encountered when using multiwavelets in applications, and we propose new solutions for the design of multiwavelets filter banks by introducing the so-called balanced multiwavelets     

Biorthogonal Multiwavelets with Sampling Property and Application in Image Compression

This paper discusses biorthogonal multiwavelets with sampling property. In such systems, vector-valued refinable functions act as the sinc function in the Shannon sampling theorem, and their corresponding matrix-valued masks possess a special structure. In particular, for the multiplicity \(r=2\), a biorthogonal multifilter bank can be reduced to two scalar-valued filters. Moreover, if the vector-valued scaling functions are interpolating, three different concepts: balancing order, approximation order and analysis-ready order, will be shown to be equivalent. Based on this result, we introduce the transferring armlet order for constructing biorthogonal balanced multiwavelets with sampling property. Also, some balanced biorthogonal multiwavelets will be obtained. Finally, application of biorthogonal interpolating multiwavelets in image compression is discussed. Experiments show that for the same length, the biorthogonal multifilter bank is superior to the orthogonal case. Moreover, certain biorthogonal interpolating multiwavelets are also better than the classical Daubechies wavelets.     

Context- and HVS-Based Multiwavelet Image Coding Using SPIHT Framework

In this paper, multiwavelets are considered in the context of image compression based on the human vision system (HVS). First, selecting the BSA (4/4)* filters, a twodimensional image is transformed with our proposed algorithm I. Second, we apply HVS coefficients into the subbands of the transformed image. Third, we split the coefficients into two parts: the significance map and residue map. Then a new modified set partitioning in hierarchical trees (SPIHT) algorithm is proposed to encode the significance map. Fourth, algorithm III is presented for coding the residue map. Finally, we adopt context-based adaptive arithmetic coding to encode the bit stream. We also provide some experimental results proving that multiwavelets are worth studying and compare them with those of other multiwavelet and JPEG2000 algorithms.