由小波变换的模极大值快速重构信号

本文从多尺度分析的思想出发，提出一种由信号小波变换的模极大值快速重构信号的方法，在不同尺度上，以阶跃函数在该尺度上的小波变换作为基函数，利用模极大值拟合信号的小波变换，然后进行小波反演得到重构信号。这种快速算法具有明确而直观的物理意义，实现简单方便。文中还给出了对重构信号的误差修正方法，数值方法的结果表明，这种快速重构算法对不同类型的信号同样有效。     

重构小波系数的分段三次样条插值新算法

利用小波变换模极大值原理对信号去噪之后,如何由保留下来的模极大值点恢复出满意的重构信号,是一个重要课题.本文首先分析模极大值与小波系数之间的内在关系,提出了模极大值实际上是小波系数在特定意义下的离散采样;然后给出了一种对模极大值进行预处理的方法,由此得到了一组新的伪模极大值序列;利用这组伪模极大值序列,提出了一种新的重构小波系数的分段三次样条插值(PCSI)新算法,该算法程序简单,易实现,克服了交替投影(AP)法计算量大、程序复杂等缺点;最后给出一个应用实例,实验结果表明,与经典的交替投影法相比,本文提出的PCSI算法可获得更高的重构信号信噪比增益和更小的相对均方误差,它是一种实际、有效的算法.     

模极大值降噪法在信号降噪中的应用

利用信号与噪声奇异点Lipschitz指数的区别,以及反映在其小波变换模极大值曲线上的特点,应用小波变换模极大值降噪法,对含有带限高斯白噪声的数字通信信号进行了降噪处理,并对降噪原理、算法和仿真结果进行了较为详细的分析。提出了一种信号重构新方法,该方法利用小波变换对信号和噪声的模极大值进行分离,通过对噪声模极大值对应的小波系数进行线性压缩后重构信号,并用仿真试验验证了该方法的有效性。     

重构小波系数的分段三次样条播值新算法

利用小波变换模极大值原理对信号去噪之后,如何由保留下来的模极大值点恢复出满意的重构信号,是一个重要课题。本文首先分析模极大值与小波系数之间的内在关系,提出了模极大值实际上是小波系数在特定意义下的离散采样;然后给出了一种对模极大值进行预处理的方法,由此得到了一组新的伪模极大值序列;利用这组伪模极大值序列,提出了一种新的重构小波系数的分段三次样条播值（ＰＣＳＩ）新算法,该算法程序简单,易实现,克服了交替投影（ＡＰ）法计算量大、程序复杂等缺点;最后给出一个应用实例,实验结果表明,与经典的交替投影法相比,本文提出的ＰＣＳＩ算法可获得更高的重构信号信噪比增益和更小的相对均方误差,它是一种实际、有效的算法。     

小波变换域滤波方法在电磁生物医学成像中的应用

电磁生物医学成像信号是一种非平稳信号,传统滤波方法全造成信号重要信息的损失。小波变换局部极大值滤波方法利用信号与噪声不同的尺度变化特性来区分信号与噪声,将噪声从信号中分离出来。小波变换局部极大值描述是信号的一种稳定的、近似的描述,可以利用交替投影算法从小波变换局部极大值描述来重构信号。ａｄｈｏｃ算法是寻找小波变换对数模极大线的一种有效算法,在此基础上,提出模极大值漂移抑制方法,对生物医学成人像仿真     

基于信号奇异性分析的小目标检测方法

提出了一种新的基于信号奇异性分析的小目标检测方法，该方法将图像中的小目标看作是图像信号中的奇异点(突变点)，利用小波变换模极大值点同信号奇异点之间的对应关系，结合信号奇异性与模极大值在多尺度上的变化规律，实现噪声抑制和信号增强，然后通过区域分析，检测图像小波变换模极大值，进而实现小目标检测。实验结果证明该方法是行之有效的。     

用小波变换的模极大值提取调制信号频率

利用小波变换系数的模值与信号奇异性指数之间的关系,从调频信号中提取出调制信号的频率.其方法是:对调频信号进行小波变换,取适当尺度上的小波系数进行平方,得到小波变换模极大值的分布曲线,对该曲线进行小波强制滤波,得到反映调制信号频率的光滑曲线,计算该曲线的频率,即可得调制信号的频率.经过计算机仿真,证明该方法是可行的.     

基于反对称双正交小波分解系数的模极大值的信号快速重构

因为反对称双正交小波具有近似微分算子性质,该文用它对信号作无下采样(Un-decimated)的小波变换,以此获得信号在各尺度下与信号的"边缘"点相对应的局部模极大值.在只保留这些局部模极大值(即边缘)点信息的条件下,利用高斯函数直接拟合各级小波系数,然后再作小波逆变换就可恢复原信号.实验表明,与现有的采用二进小波变换的方法比较,该方法更加简便快捷.     

基于RBF网络的小波变换模极大值重构算法

本文根据交替投影的基本思想,提出了一种基于径向基函数网络的小波变换模极大值重构方法.该方法利用径向基函数网络(RBFN)在其基函数宽度很大时具有较好的线性映射这一特性来加快收敛速度,提高重构精度.它不仅能较好地重构信号的边缘,而且能准确地重构出信号的峰值.大量仿真实验表明,该方法对各种信号是普遍适用的,具有收敛速度快,重构精度高的特点.     

基于Hermite插值的小波模极大值重构滤波的肌电信号消噪方法

为了消除混杂在肌电信号中的噪声,该文提出了基于Hermite插值的小波模极大值重构滤波的肌电信号消噪方法.该方法先对肌电信号进行小波分解;其次,根据小波系数的奇异性,利用信号与噪声模极大值在小波尺度上的不同变化特性,分离出信号与噪声;再次,用Hermite插值法重构小波系数;最后从重构的小波系数恢复成去噪后的信号.实验结果表明,Hermite插值的小波模极大值重构能有效地去除噪声,提高信噪比,且保留了肌电信号的细节信息,为肌电信号的特征提取和模式识别创造了良好的条件.     

一种改进的稀疏信道估计算法

文中在匹配跟踪算法的基础上实现了一种稀疏信道估计的改进算法。该算法首先通过正交匹配跟踪得到信道非零抽头的粗略估计,并依此来设置自适应均衡器的权重系数的初始值,进行自适应的调整和校正,最终实现对实际信道冲激响应的精确逼近。这样不仅避免了对无谓零抽头的估计,而且提高了信道估计的性能。     

Statistical study of the wavelet analysis of fractional Brownianmotion

We present a statistical study of wavelet coefficients of a fractional Brownian motion. A central limit theorem for empirical variances of exact wavelet coefficients is given. Under conditions on the mother wavelet and the choice of scales, a limit theorem is given for fitted wavelet coefficients computed from a time series. It provides an estimator for the self-similarity parameter of Gaussian time series     

数字电视系统中OFDM稀疏信道估计算法

针对采用OFDM调制技术的数字电视传输系统，利用信道的稀疏特性提出一种基于子空间拟合的信道估计算法。该算法首先利用参考矩阵列向量与观测向量的相关性来确定信道的非零抽头位置，然后再采用最小二乘算法完成对非零系数值的二次估计，避免了无谓的零抽头估计，改善了算法性能。在低信噪比和导频数较少的情况下，算法仍具有稳健的性能，仿真结果验证了该算法的有效性。     

基于小波变换的语音压缩感知处理

文章首先简单介绍了压缩感知(CS)理论框架,然后根据语音信号小波变换系数的特点,提出了改进的压缩感知算法,对高频系数进行压缩处理,低频系数不变.采用基追踪算法重构出高频系数,再利用小波反变换得到原始语音信号.实验结果表明,在相同的测量点数下,本文的算法比原有CS算法在重构语音的信噪比和MOS分上都有较大的提升.     

A Video Coding Algorithm Based on Intraframe and Interframe Joint Prediction of Wavelet Coefficients

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A Video Coding Algorithm Based on Intraframe and Interframe Joint Prediction of Wavelet Coeffictients

A novel video coding algorithm based on intraframe and interframe prediction of wavelet coefficients is described in this paper.A BZT(Block Zero Tree)coding scheme represents the position of zero coefficients block efficiently,For nonzero coefficients block,temporal redundancy is removed using MultiResolution Motion Estimation(MRME).The proposed algorithm improves the coding performance significantly over the baseline MRME technique.In addition,the computational complexity is further reduced.     

MR image reconstruction based on comprehensive sparse prior

In this paper, a novel Magnetic Resonance (MR) reconstruction framework which combines image-wise and patch-wise sparse prior is proposed. For addressing, a truncated beta-Bernoulli process is firstly employed to enforce sparsity on overlapping image patches emphasizing local structures. Due to its properties, beta-Bernoulli process can adaptive infer the sparsity (number of nonzero coefficients) of each patch, an appropriate dictionary, and the noise variance simultaneously, which are prerequisite for iterative image reconstruction. Secondly, a General Gaussian Distribution (GGD) prior is introduced to engage image-wise sparsity for wavelet coefficients, which can be then estimated by a threshold denoising algorithm. Finally, MR image is reconstructed by patch-wise estimation, image-wise estimation and under-sampled k-space data with least square data fitting. Experimental results have demonstrated that proposed approach exhibits excellent reconstruction performance. Moreover, if the image is full of similar low-dimensional-structures, proposed algorithm has dramatically improved Peak Signal to Noise Ratio (PSNR) 7～9 dB, with comparisons to other state-of-art compressive sampling methods.     

Efficient sign coding and estimation of zero-quantized coefficients in embedded wavelet image codecs

Wavelet transform coefficients are defined by both a magnitude and a sign. While efficient algorithms exist for coding the transform coefficient magnitudes, current wavelet image coding algorithms are not as efficient at coding the sign of the transform coefficients. It is generally assumed that there is no compression gain to be obtained from entropy coding of the sign. Only recently have some authors begun to investigate this component of wavelet image coding. In this paper, sign coding is examined in detail in the context of an embedded wavelet image coder. In addition to using intraband wavelet coefficients in a sign coding context model, a projection technique is described that allows nonintraband wavelet coefficients to be incorporated into the context model. At the decoder, accumulated sign prediction statistics are also used to derive improved reconstruction estimates for zero-quantized coefficients. These techniques are shown to yield PSNR improvements averaging 0.3 dB, and are applicable to any genre of embedded wavelet image codec.     

Image modeling using interscale phase properties of complex wavelet coefficients.

This paper describes an approach to image modelling using interscale phase relationships of wavelet coefficients for use in image estimation applications. The method is based on the dual tree complex wavelet transform, but a phase rotation is applied to the coefficients to create complex "derotated" coefficients. These derotated coefficients are shown to have increased correlation compared to standard wavelet coefficients near edge and ridge features allowing improved signal estimation in these areas. The nature of the benefits brought by the derotated coefficients are analyzed and the implications for image estimation algorithm design noted. The observations and conclusions provide a basis for design of the denoising algorithm in [1].