适宜图像编码的双正交小波基的选择

提出一种新的选择适合图橡编码应用的双正交小波基的方法。通过用几个已证实是与图像编码密切相关的小波基评价标准对小波进行全面评价，选出了一些适宜图像编码应用的双正交小波基，并作了编码模拟检验。     

M-band biorthogonal interpolating wavelets via lifting scheme

Recently, the lifting scheme was generalized to the multidimensional and multiband cases and was used to design M-band interpolating scaling filters and their duals. Based on this idea, we develop a new lifting pattern, namely, the progressive lifting pattern. This pattern allows us to pairwise generate M-band interpolating filterbanks and wavelets by the order from lowpass to highpass filters. A complete lifting procedure is divided into M - 1 simple steps, in each step, a pair of filters (the l'th filter and its dual) are generated. In this way, an M -band biorthogonal interpolating filterbank/wavelet is determined by M(M - 1) lifting filters. The first 2(M 1) lifting filters completely characterize the two scaling filters as well as the vanishing moments of bandpass and highpass filters; the residual (M - 1) (M - 2) lifting filters are used to pairwise optimize the bandpass and highpass filters in terms of the criterion of stopband energy minimization. The obtained M-band biorthogonal interpolating filterbanks and wavelets provide excellent frequency characteristics, in particular, low stopband sidelobes. Furthermore, the pattern is also utilized to design signal-adapted interpolating filterbanks and their rational coefficient counterparts in terms of subband coding gain. The obtained filterbanks achieve large subband coding gains. The rational coefficient filterbanks preserve the biorthogonality and allow wavelet transforms from integers to integers and a unifying lossy/lossless coding framework at the cost of a slight degradation in subband coding gain.     

三带自适应提升双正交滤波器组

该文研究了利用三带提升方法设计三带自适应双正交的滤波器组。在设计中,用子带编码增益作为设计准则,从任意一个滤波器组(标准正交或双正交)开始。通过有序自适应提升方法来设计三带双正交滤波器组。最后。给出例子说明。当选择一个合适初始滤波器组时,子带码增益可以得到较大提高。     

分析与综合小波交换使用时编码性能的研究

本文提出一种新的选择适于图像编码应用的双正交小波基的方法。通过用几个已被证实是与图像编码密切相关的小波基评价标准,对双正交小波中分析与综合函数交换使用时的编码性能进行全面的比较研究,选出了适合图像编码的分析或综合小波基,并作了编码实验检验。     

航空图像压缩的双正交小波滤波器整数化设计

在航空图像压缩中,通常采用具有线性相位、正则性、消失矩和完全重构,及适于硬件实现、实时等特性的小波。根据小波滤波器设计,提出了一种基于图像压缩的构造整数双正交小波滤波器的设计方法。从选择小波基的原则为出发点,以CDF9-7小波基为参考,以压缩效果为准则来构造出更优的双正交整数小波基,并且采用航空图像为标准训练图像,以压缩比、峰值信噪比、压缩后保留能量百分比为参数,来寻找最优的小波基。试验结果证明,此方法可以实施非常简单的、无浮点乘法的运算,因而减少运算复杂性以及降低小波硬件实现的难度。     

Wavelet-based very low bit-rate video coding using image warpingand overlapped block motion compensation

The authors present an algorithm for very low bit-rate video coding that combines new ideas in motion estimation, wavelet filter design, and wavelet-based coding techniques. A new motion compensation technique using image warping and overlapped block motion compensation is proposed to reduce temporal redundancies in a given image sequence. This combined motion model has the advantage of representing more complex motion than simple block matching schemes. To further improve the quality of the temporal prediction, an adaptive grid with variable density according to the varying motion activity of a given scene is generated. An adaptively switched high-quality texture interpolation is employed to cope with the problem of fractional displacements in such a way that both objective and subjective reconstruction quality is improved. Spatial decorrelation of the motion compensated residual images is performed using an one-parametric family of biorthogonal infinite impulse response (IIR) wavelet filters coupled with the highly efficient pre-coding scheme of `partitioning, aggregation and conditional coding' (PACC). Experimental results demonstrate significant improvements in objective quality of 1.0-2.3 dB PSNR in comparison to the H.263+ test model TMN10 using advanced coding options. In addition, the authors' intracoding method provides a performance gain of 0.5 dB PSNR on the average for a test suite of various still images when compared to the emerging still image coding standard JPEG-2000     

A tutorial on modern lossy wavelet image compression: foundationsof JPEG 2000

One of the purposes of this article is to give a general audience sufficient background into the details and techniques of wavelet coding to better understand the JPEG 2000 standard. The focus is on the fundamental principles of wavelet coding and not the actual standard itself. Some of the confusing design choices made in wavelet coders are explained. There are two types of filter choices: orthogonal and biorthogonal. Orthogonal filters have the property that there are energy or norm preserving. Nevertheless, modern wavelet coders use biorthogonal filters which do not preserve energy. Reasons for these specific design choices are explained. Another purpose of this article is to compare and contrast “early” wavelet coding with “modern” wavelet coding. This article compares the techniques of the modern wavelet coders to the subband coding techniques so that the reader can appreciate how different modern wavelet coding is from early wavelet coding. It discusses basic properties of the wavelet transform which are pertinent to image compression. It builds on the background material in generic transform coding given, shows that boundary effects motivate the use of biorthogonal wavelets, and introduces the symmetric wavelet transform. Subband coding or “early” wavelet coding method is discussed followed by an explanation of the EZW coding algorithm. Other modern wavelet coders that extend the ideas found in the EZW algorithm are also described     

小波提升格式的研究

小波提升格式以计算快速、能形成整数到整数的可逆变换的优势在数字图像压缩领域得到了广泛应用,而如何把适合于图像压缩的第一代小波映射成整数提升格式也成为一个研究问题。本文应用双正交滤波的多相矩阵的多步三角分解,提出不同多相矩阵表示时寻求提升系数的方法,并利用这种方法给出了多相矩阵的行列式不为1的滤波器组的提升格式。     

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions—the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of ${rm L}^2({BBR})$ by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of ${rm L}^2({BBR}^2)$, we then discuss a methodology for constructing 2-D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1-D counterpart, we relate the real and imaginary components of these complex wavelets using a multidimensional extension of the HT—the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efficient fast Fourier transform (FFT)-based filterbank algorithm for implementing the associated complex wavelet transform.      

一种改进的零树结构编码算法研究

现在大部分图像压缩技术都利用了小波变换后图像不同分辨率反相同方向子带之间的相关性。采用双正交提升小波将图像变换到小波域,通过增加熵编码的符号集,提出了一种基于正交小波变换的增广零树压缩编码算法,在整个编译码过程中仅使用一个系数列表,况且不进行任何排序操作。通过相关实验,证实该方法能有效进行图像压缩,提高了压缩率。     

基于小波分析的分形参数估计新方法

该文研究目的是估计1/f类分形随机过程参数矢量 (, 2,2w)。作者基于小波分析,对1/f过程观测值的小波系数方差进行一系列代数运算,并给出详尽的证明过程,最终求取了噪声中分数布朗运动(fBm)参数矢量的估计量。实验结果表明,与传统的极大似然估计(ML)相比,算法简洁,效果良好,估计参数范围广泛,同时对噪声也不再局限于高斯分布。     

Optimization Design of Biorthogonal Wavelet Filter Banks for Extending JPEG 2000 Standard Part-2

A generic optimization design approach of biorthogonal wavelet filter banks (BWFB) for extending the JPEG 2000 standard part-2 is presented in this paper. This approach adopts Vaidyanathan optimal coding gain criterion to design the BWFB, and adopts peak signal-to-noise ratio (PSNR) as the criterion to optimize this BWFB. A functional relation between the general BWFB and their lifting scheme is derived in the first place with respect to one free variable, so that the optimization design of the BWFB is easier and more convenient. In addition, a general image model is formulated as a first-order Markov process driven by Gaussian white noise. It is taken as an input of two-channel filter banks which satisfy perfect reconstruction (PR) condition to realize subband coding for obtaining the optimal BWFB according to the Vaidyanathan optimal coding gain criterion. Finally, a new 9/7 BWFB with rational coefficients is proposed for extending the JPEG 2000 standard part-2, with PSNR of reconstructed images only 0.20 dB lower than standard CDF 9/7 BWFB for infrared thermal image compressions.     

基于多尺度Wiener滤波器的分形噪声滤波

针对淹没在1/f噪声中的有用信号恢复问题,本文提出了一套基于双正交小波变换与Wiener滤波的多尺度滤波算法,并设计出多尺度Wiener滤波器.首先,利用双正交小波变换将带有1/f噪声的信号分解成多尺度的子带信号,通过小波变换对1/f噪声的白化作用,消除了1/f噪声的非平稳性、自相似性和长程相关性.其次,在小波域内,利用Wiener滤波,实现了噪声和有用信号的分离,估计出了各子带中的有用信号.最后,利用双正交小波的精确重构性,较好地恢复出淹没在1/f噪声中的有用信号.仿真实验表明,该滤波器能有效的抑制分形噪声,显著地提高信噪比.     

基于块区域子波变换的甚低码率视频编码算法

本文描述了一个有效的视频编码算法，该算法基于视频信号的分数像素精度重叠运动补偿预测和利用双正交滤波器组的区域子波分解，文中给出了采用２４＊２４重叠块的编码器模拟结果。     

基于内嵌小波变换的遥感图像编码

本文针对遥感图像的数据特点,提出了结合双正交小波变换和改进SPIHT算法的内嵌小波编码方案.实验结果表明,本文的方法能够在几乎不降低恢复图像质量的前提下降低了计算复杂度,提高了编码速度,有利于实时编码.     

一种新的小波分形变换图像编码算法

提出了一种基于平滑双正交小波和自适应分割算法的小波域分形图像编码算法，在基于离散有限方差(DFV)最优准则下得到了适合图像编码的一种新的平滑双正交小波，从而改善了分块效应。在小波域的分形编码中，提出了一种基于图像信息分布特征的自适应分割算法，实验表明，该文算法在相同压缩比的情况下，解码图像的主观视觉质量和峰值信噪比都明显优于SQS方法、基本分形图像编码方法和SPIHT方法。     

17/11双正交小波的优化设计及其对图像压缩性能的分析

许多适合于图像编码的小波,如CDF-9/7,Winger-17/11(W-17/11),Villasenor-6/10和10/18(V-6/10和V-10/18)小波,其滤波器系数是无理数,需要用无限的计算精度实现对应的离散小波变换(DWT)。该文给出了一种参数化构造17/11双正交小波组的简便方法：首先把小波合成滤波器表示为用两个自由参数表达的三角多项式,然后把双正交小波的精确重构条件归结为一个线性方程组,最后求解此方程组得到对应的小波分解滤波器,从而得到了17/11双正交小波滤波器的参数表达式。通过调整表达式中的自由参数,可以随意构造具有所需特征的17/11线性相位小波滤波器。作为构造实例,构造出一种新的有理系数17/11双正交小波滤波器,它具有优化的编码增益。实验表明：其压缩性能与W-17/11和V-10/18小波滤波器相当,优于CDF-9/7和V-6/10小波滤波器。     

基于双小波系数测量有效值

从双正交小波出发,得出利用双正交小波及正交小波系数求电压、电流有效值的公式,并进行了离散化,同时对一电压信号进行了数字仿真,最后对结果进行了分析和研究。     

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。