Efficient computation of the discrete autocorrelation wavelet inner product matrix

Discrete autocorrelation (a.c.) wavelets have recently been applied in the statistical analysis of locally stationary time series for local spectral modelling and estimation. This article proposes a fast recursive construction of the inner product matrix of discrete a.c. wavelets which is required by the statistical analysis. The recursion connects neighbouring elements on diagonals of the inner product matrix using a two-scale property of the a.c. wavelets. The recursive method is an (log (N)³) operation which compares favourably with the (N log N) operations required by the brute force approach. We conclude by describing an efficient construction of the inner product matrix in the (separable) two-dimensional case.     

结合图像属性的MSD-FICA盲水印算法

基于图像高频子分量相互独立的属性,再结合图像低频能量不易丢失的特点,该文设计了多分辨率子带分解的快速独立分量分析(MSD-FICA)盲水印算法,借鉴了经典的量化调制水印(QIM)算法思想,对原始图像小波分解后的高频成分(水平、垂直、对角小波系数)进行排序,取中频成分。嵌入水印是对中频分量系数和低频分量系数同时嵌入,水印的提取采用快速独立分量分析(FICA)算法,先用主成分分析进行预处理,然后用FICA盲提取水印。实验表明,该算法能有效地提取出水印,并能抵抗一定的压缩、滤波、噪声攻击。     

Multivariate Bayes Wavelet shrinkage and applications

In recent years, wavelet shrinkage has become a very appealing method for data de-noising and density function estimation. In particular, Bayesian modelling via hierarchical priors has introduced novel approaches for Wavelet analysis that had become very popular, and are very competitive with standard hard or soft thresholding rules. In this sense, this paper proposes a hierarchical prior that is elicited on the model parameters describing the wavelet coefficients after applying a Discrete Wavelet Transformation (DWT). In difference to other approaches, the prior proposes a multivariate Normal distribution with a covariance matrix that allows for correlations among Wavelet coefficients corresponding to the same level of detail. In addition, an extra scale parameter is incorporated that permits an additional shrinkage level over the coefficients. The posterior distribution for this shrinkage procedure is not available in closed form but it is easily sampled through Markov chain Monte Carlo (MCMC) methods. Applications on a set of test signals and two noisy signals are presented.     

液压系统故障信号的小波包检测方法

提出了一种利用小波包检测调速阀故障信号的方法。通过小波的小波包分析将信号按一定的尺度进行划分,不同频率的信号被划分到不同的频段中。由经过预处理的信号经过小波包分解与重构后,可以得到小波包重构图,由图中可以获得故障产生的时间点和频率,再对故障的严重程度进行了量化分析。实验结果表明用小波包理论进行故障检测是可行的。     

Factored principal components analysis, with applications to face recognition

A dimension reduction technique is proposed for matrix data, with applications to face recognition from images. In particular, we propose a factored covariance model for the data under study, estimate the parameters using maximum likelihood, and then carry out eigendecompositions of the estimated covariance matrix. We call the resulting method factored principal components analysis. We also develop a method for classification using a likelihood ratio criterion, which has previously been used for evaluating the strength of forensic evidence. The methodology is illustrated with applications in face recognition.     

随机过程多尺度分析与一类算子表示

本文分析了二阶矩过程多尺度分析,给出了定义及一些性质,利用算子方法分析过程的小波展开问题.     

A wavelet method for unfolding sphere size distributions

The authors consider the problem of estimating the density of the radii of spheres in a medium, based on their observed random cross‐sections. This problem is known as Wicksell's corpuscle problem. The authors first convert Wicksell's integral equation to a form suitable for the application of thresholding wavelet methods to solve ill‐posed integral equations, given noisy data. They then derive the asymptotic properties of their estimators and compare them with other methods available via a Monte Carlo simulation study. They also illustrate their approach with some real data.     

A wavelet-based time-varying autoregressive model for non-stationary and irregular time series

In this work we propose an autoregressive model with parameters varying in time applied to irregularly spaced non-stationary time series. We expand all the functional parameters in a wavelet basis and estimate the coefficients by least squares after truncation at a suitable resolution level. We also present some simulations in order to evaluate both the estimation method and the model behavior on finite samples. Applications to silicates and nitrites irregularly observed data are provided as well.     

Posterior probability intervals for wavelet thresholding

Summary. We use cumulants to derive Bayesian credible intervals for wavelet regression estimates. The first four cumulants of the posterior distribution of the estimates are expressed in terms of the observed data and integer powers of the mother wavelet functions. These powers are closely approximated by linear combinations of wavelet scaling functions at an appropriate finer scale. Hence, a suitable modification of the discrete wavelet transform allows the posterior cumulants to be found efficiently for any given data set. Johnson transformations then yield the credible intervals themselves. Simulations show that these intervals have good coverage rates, even when the underlying function is inhomogeneous, where standard methods fail. In the case where the curve is smooth, the performance of our intervals remains competitive with established nonparametric regression methods.