We propose a new “Haar-Fisz” technique for estimating the time-varying, piecewise constant local variance of a locally stationary Gaussian time series. We apply our technique to the estimation of the spectral structure in the Locally Stationary Wavelet model. Our method combines Haar wavelets and the variance stabilizing Fisz transform. The resulting estimator is mean-square consistent, rapidly...

In our previous work, we showed empirically that independent (Haar) wavelet models were parsimonious, computationally efficient and accurate in modeling heterogeneous network traffic measured by both auto-covariance functions and buffer loss rate. We also proved analytically that such models were capable of capturing any decay rate of auto-covariance functions at large lags. But the simplicity ...

The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar bases generated by multiresolution analysis. Bases consist of three piecewise constant wavelet functions with a support $[0,1] \times [0,1] $.

With the development of steganalysis, the security of steganography is faced with tremendous challenge. High order statistical analysis is an effective and common detecting method that can defeat many hiding scheme. This paper proposes a secure steganography that can effectively resist image steganalysis based on high order statistical analysis. We have analyzed Haar wavelet decomposition chara...

Metode Wavelet merupakan salah satu metode yang unggul untuk menganalisis serta mengekstraksi ciri isyarat suara tutur. Dalam proses ekstraksi menggunakan Wavelet, terdapat beberapa faktor dapat berpengaruh dalam mendapatkan bersifat diskriminan, diantaranya: pemilihan mother wavelet, sub-band, dan level dekomposisi. Beberapa contoh sering digunakan Daubechies, Coiflet, Meyer, Haar, Symlet, Bio...

An orthogonal Haar scattering transform is a deep network computed with a hierarchy of additions, subtractions and absolute values over pairs of coefficients. Unsupervised learning optimizes Haar pairs to obtain sparse representations of training data with an algorithm of polynomial complexity. For signals defined on a graph, a Haar scattering is computed by cascading orthogonal Haar wavelet tr...

The formulation and implementation of wavelet based methods for the solution of multidimensional partial differential equations in complex geometries is discussed. Utilizing the close connection between Daubechies wavelets and finite difference methods on arbitrary grids, we formulate a wavelet based collocation method, well suited for dealing with general boundary conditions and nonlinearities...

It is well known that the Haar and Shannon wavelets in L2(R) are at opposite extremes, in the sense that the Haar wavelet is localized in time but not in frequency, whereas the Shannon wavelet is localized in freqency but not in time. We present a rich setting where the Haar and Shannon wavelets coincide and are localized both in time and in frequency. More generally, if R is replaced by a grou...