The application of the wavelet transform in image processing is most frequently based on a separable transform. Lines and columns in an image are treated independently and the basis functions are simply products of corresponding onedimensional functions. Such a method keeps simplicity in design and computation. In this paper, a new two-dimensional approach is proposed, which retains the simplic...

This paper addresses the problem of choosing the optimal number of basis functions in constructing wavelet series density estimators. It is well known that projection estimators tend to overrt the density if the number of basis functions in the orthogonal expansion is too large. In extreme cases the estimator is close to the Dirac function concentrated at the observations. We propose a roughnes...

Orthogonal and Symmetric Haar Wavelets on the Sphere Christian Lessig Master of Science Graduate Department of Computer Science University of Toronto 2007 The efficient representation of signals defined over spherical domains has many applications. We derive a new spherical Haar wavelet basis (SOHO) that is both orthogonal and symmetric, rebutting previous work that presumed the nonexistence of...

Orthogonal and Symmetric Haar Wavelets on the Sphere Christian Lessig Master of Science Graduate Department of Computer Science University of Toronto 2007 The efficient representation of signals defined over spherical domains has many applications. We derive a new spherical Haar wavelet basis (SOHO) that is both orthogonal and symmetric, rebutting previous work that presumed the nonexistence of...

This paper presents an innovative method for detecting and classifying various power system disturbances using wavelet analysis. The proposed method employs a multiresolution analysis (MRA) using localized wavelet basis functions. The nonlinear sub-band time-frequency structure extracted using the MRA can provide the needed features to detect and classify any power system transient disturbance....

A simple construction of an orthonormal basis starting with a so called mother wavelet, together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications. An orthonormal basis may not, however, always be a suitable representation of a signal, particularly when time (or space) invariance is a required property. ...

Function approximation, which finds the underlying relationship from a given finite input-output data is the fundamental problem in a vast majority of real world applications, such as prediction, pattern recognition, data mining and classification. Various methods have been developed to address this problem, where one of them is by using artificial neural networks. In this paper, the radial bas...

The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the wavelet based on power. The spectral density has physical units which may be related to the squared amplitude of the signal, as do its margins the mean wavelet pow...

A novel approach to the removal of noise from threedimensional image data is described. The image sequence is represented using a non-adaptive wavelet basis, carefully chosen for its ability to compactly represent locally planar surfaces. This is important in many 3-D applications, including video sequences, where they represent moving luminance edges, and medical volume data, where they repres...

The anisotropic wavelet packet transform is an extension of the conventional wavelet (packet) transform where the basis can have di erent scales in di erent dimensions. As there are certain kinds of images with di erent behaviour in horizontal and vertical direction, anisotropic wavelet packet bases can be adapted more precisely to these images. Zero-tree image compression has already proved it...