linear filters are used for a wide range of magnetic science including noise attenuation, spatial derivatives, upward and downward continuation and reduction to the pole. the majority of these filters are spatially-invariant, meaning that the filter has a constant wave number response over the whole signal. in contrast, many signals which encountered real problems such as magnetic signals, typi...

The training algorithm of Wavelet Neural Networks (WNN) is a bottleneck which impacts on the accuracy of the final WNN model. Several methods have been proposed for training the WNNs. From the perspective of our research, most of these algorithms are iterative and need to adjust all the parameters of WNN. This paper proposes a one-step learning method which changes the weights between hidden la...

In this paper we present a novel wavelet based exchange rate forecast model integrating wavelet filters for denoising and Improved Instance Based Learning(IIBL) approach. The proposed model implements a novel technique that extends the nearest neighbor algorithm to include the concept of pattern matching so as to identify similar instances thus implementing a nonparametric regression approach.T...

The problem of change detection of time series with abrupt and smooth changes in the spectral characteristics is addressed. We first review the main characteristics of the discrete wavelet transform and the maximal overlap discrete wavelet transform. An algorithm for sequential change detection in time series is then reported based on the maximal overlap discrete wavelet transform and Bayesian ...

We consider the recent suggestion that spectrum estimation can be accomplished by applying wavelet denoising methodology to wavelet packet coefficients derived from the logarithm of a spectrum estimate. The particular algorithm we consider consists of computing the logarithm of the multitaper spectrum estimator, applying an orthonormal transform derived from a wavelet packet table to the log mu...

An exact solution of the homogeneous wave equation, which was found previously, is treated from the point of view of continuous wavelet analysis (CWA). If time is a fixed parameter, the solution represents a new multidimensional mother wavelet for the CWA. Both the wavelet and its Fourier transform are given by explicit formulas and are exponentially localized. The wavelet is directional. The w...

Since the last decade the study of the wavelet transform has attracted many efforts and made great progresses. However, the research interest is still growing. In this thesis, we investigate the applications of the wavelet transform to image and video processing. We first study the wavelet transform mainly from a statistical point of view. Specifically, we study the statistics of the wavelet co...

A wavelet is a basis function used to construct a wavelet transform. The first known wavelet – Haar wavelet was proposed in 1909 by Alfred Haar. Wavelet theory has been applied to various problems including signal processing in communications, image compression-extraction, solution of the linear and nonlinear integral equations etc. Haar wavelet based discretization technique is adopted for sol...

In many applications it is desirable to study nonorthogonal wavelet transforms. A translation-invariant wavelet transform is a nonorthogonal variant of the classical wavelet transform which plays an important role in denoising algorithms. However, it has been observed in many experiments that the thresholding scheme for the orthogonal DWT should be slightly modiied for use in the translation-in...

This paper studies the adaptive wavelet design for fabric defect detection. In order to achieve translation invariance and more flexible design, the wavelet design focused on nonsubsampled wavelet transform. We design the wavelet filters under the constraints that the analysis filters are power complementary, and the wavelet has only one vanishing moment, which corresponds to a multiscale edge ...