The three-dimensional biorthogonal multi-resolution time-domain (Bi-MRTD) method is presented for both free-space and half-space scattering problems. The perfectly matched layer (PML) is used as an absorbing boundary condition. It has been shown that improved numerical-dispersion properties can be obtained with the use of smooth, compactly-supported wavelet functions as the basis, where here we...

Field seismic data can contain many sorts of noise and interferences. If the noise is stronger in order of magnitude than the signal, most techniques often applied in seismic processing will be severely affected. Denoising methods, even very robust schemes such as physical wavelet frame denoising (PWFD), are not exceptions. In this paper, we present a robust, data adaptive and fast 1D wavelet t...

Digital watermarking is a solution to the problem of copyright protection and authentication of multimedia data while working in a networked environment. We propose a robust quantization-based image watermarking scheme, called the gradient direction watermarking (GDWM), and based on the uniform quantization of the direction of gradient vectors. In GDWM, the watermark bits are embedded by quanti...

Abstract Spectral graph wavelets introduce a notion of scale in networks, and are thus used to obtain a local view of the network from each node. By carefully constructing a wavelet filter function for these wavelets, a multi-scale community detection method for monoplex networks has already been developed. This construction takes advantage of the partitioning properties of the network Laplacia...

In the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are preferable. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang [2]. A cha...

We show that imposing a certain number of vanishing moments on a scaling function (e.g., coiflets) leads to fairly small phase distortion on its associated filter bank in the neighborhood of DC. However, the phase distortion at the other frequencies can be much larger. We design a new class of real-valued, compactly supported, orthonormal, and nearly symmetric wavelets (we call them generalized...

Wavelet shrinkage is an effective nonparametric regression technique, especially when the underlying curve has irregular features such as spikes or discontinuities. The basic idea is simple: take the discrete wavelet transform (DWT) of data consisting of a signal corrupted by noise; shrink or remove the wavelet coefficients to remove the noise; and then invert the DWT to form an estimate of the...

In this letter we propose a facial feature extraction technique which utilizes polynomial coefficients derived from 2D Discrete Cosine Transform (DCT) coefficients obtained from horizontally and vertically neighbouring blocks. Face authentication results on the VidTIMIT database suggest that the proposed feature set is superior (in terms of robustness to illumination changes and discrimination ...

In this paper we introduce the DCT-mod2 facial feature extraction technique which utilizes polynomial coefficients derived from 2-D DCT coefficients of spatially neighbouring blocks. We evaluate its robustness and performance against three popular feature sets for use in an identity verification system subject to illumination changes. Results on the multi-session VidTIMIT database suggest that ...

This paper concentrates on a new procedure which experimentally recognises gears and bearings faults of a typical gearbox system using a least square support vector machine (LSSVM). Two wavelet selection criteria Maximum Energy to Shannon Entropy ratio and Maximum Relative Wavelet Energy are used and compared to select an appropriate wavelet for feature extraction. The fault diagnosis method co...