We present a general framework for the design of a mother wavelet best adapted to a specific signal or to a class of signals. The filter’s coefficients are obtained via optimization of a smooth objective function. We develop an unconstrained gradient-based optimization algorithm for a discrete wavelet transform. The algorithm is extended to the joint optimization of the mother wavelet and of th...

recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. it is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. in this paper, f...

In [Found. Comput. Math., 2 (2002), pp. 203–245], Cohen, Dahmen, and DeVore proposed an adaptive wavelet algorithm for solving general operator equations. Assuming that the operator defines a boundedly invertible mapping between a Hilbert space and its dual, and that a Riesz basis of wavelet type for this Hilbert space is available, the operator equation is transformed into an equivalent well-p...

Monitoring lightning electromagnetic pulses (sferics) and other terrestrial as well as extraterrestrial transient radiation signals is of considerable interest for practical and theoretical purposes in astroand geophysics as well as meteorology. Managing a continuous flow of data, automisation of the detection and classification process is important. Features based on a combination of wavelet a...

Many state-of-the-art wavelet image coders use nonorthog-onal transforms for both lossy and lossless wavelet image coding 1, 2, 3, 4]. In this paper, a projection prediction is described that capitalizes on the non-orthogonality of wavelet transform basis vectors to improve the prediction of high-frequency coeecients. For lossy wavelet coders, the prediction yields improved context modeling and...

The generalized interpolation problem, known as the problem of reconstructing a multidimensional vector function f from a finite set of linear measures, is considered in Refs. (1) and (2). The solution of the generalized interpolation problem can be obtained as a linear combination of generating functions. Different basis functions can be used to solve the problem(3) – (7), in this paper Compac...

There are many different methods of approximating multivariate functions. We have, for example, the classic methods of polynomials, Fourier series, or tensor products, and more modern methods using wavelets, radial basis functions, multivariate splines, or ridge functions. Many of these are natural generalizations of methods developed for approximating univariate functions. However, functions o...

The collocation multiquadric radial basis functions are used to analyze static deformations of a simply supported functionally graded plate modeled by a third-order shear deformation theory. The plate material is made of two isotropic constituents with their volume fractions varying only in the thickness direction. The macroscopic response of the plate is taken to be isotropic and the effective...

Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential equations which are characterized by widely varying length scales and which are therefore hardly accessible by other numerical methods. The standard way to solve...

This paper presents Mean Best Basis algorithm, an extension of the well known Best Basis Wickerhouser’s method, for an adaptive wavelet decomposition of variable-length signals. A novel approach is used to obtain a decomposition tree of the wavelet-packet cosine hybrid transform for speech signal feature extraction. Obtained features are tested using the Polish language hidden Markov model phon...