We study image compression by a separable wavelet basis { ψ(2k1x − i)ψ(2k2y − j), φ(x − i)ψ(2k2y − j), ψ(2k1(x − i)φ(y − j), φ(x − i)φ(y − i) } , where k1, k2 ∈ Z+; i, j ∈ Z; and φ, ψ are elements of a standard biorthogonal wavelet basis in L2(R). Because k1 6= k2, the supports of the basis elements are rectangles, and the corresponding transform is known as the rectangular wavelet transform. W...

Learning can often be viewed as the problem of mapping from an input space to an output space. Examples of these mappings are used to construct a continuous function that approximates given data and generalizes for intermediate instances. Generalized Radial Basis Function (GRBF) networks are used to formulate this approximating function. A novel method is introduced that uses the Integral Wavel...

The accurate identification and classification of various power quality disturbances are keys to ensuring high-quality electrical energy. In this study, the statistical characteristics of the disturbance signal of wavelet transform coefficients and wavelet transform energy distribution constitute feature vectors. These vectors are then trained and tested using SVM multi-class algorithms. Experi...

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 this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and Schaefer in [6] and used recently in some applications (see [3]). In the case of an orthonormal basis our estimate reduces to Kadec’ optimal 1/4 re...

This paper deals with continuous frames and continuous Riesz bases. We introduce continuous Riesz bases and give some equivalent conditions for a continuous frame to be a continuous Riesz basis. It is certainly possible for a continuous frame to have only one dual. Such a continuous frame is called a Riesz-type frame [13]. We show that a continuous frame is Riesz-type if and only if it is a con...

In the present work a newer type of black box nonlinear model in Hammerstein structure is proposed. The model has Wavelet Network coupled with Orthonormal Basis Functions which is capable of modeling a class of non-linear systems with acceptable accuracy. Wavelet basis functions have the property of localization in both the time and frequency domains which enables wavelet networks to approximat...

We show how a wavelet basis may be adapted to best represent natural images in terms of sparse coefficients. The wavelet basis, which may be either complete or overcomplete, is specified by a small number of spatial functions which are repeated across space and combined in a recursive fashion so as to be self-similar across scale. These functions are adapted to minimize the estimated code lengt...