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...

ABSTRACT: This paper begins by using the Haar wavelet to analyze the cumulative distribution function of a stream of two-valued Bernoulli trials. We find that this function maps binary numbers in [0,1] into non-uniform binary numbers in [0,1]. More generally, for r-valued Bernoulli trials, the distribution function likewise maps usual base-r numbers into non-uniform base-r numbers. We also find...

By design a wavelet's strength rests in its ability to localize a process simultaneously in time-scale space. The wavelet's ability to localize a time series in time-scale space directly leads to the computational e ciency of the wavelet representation of a N N matrix operator by allowing the N largest elements of the wavelet represented operator to represent the matrix operator [Devore, et al....

This paper is a contribution to the analysis of the statistical correlation of the wavelet packet coefficients resulting from the decomposition of a random process, stationary in the wide-sense, whose power spectral density is bounded with support in [−π, π]. Consider two quadrature mirror filters (QMF) that depend on a parameter r, such that these filters tend almost everywhere to the Shannon ...

A wide variety of scientiic settings involve indirect noisy measurements where one faces a linear inverse problem in the presence of noise. Primary interest is in some function f(t) but the data is accessible only about some transform (Kf)(t), where K is some linear operator, and (Kf)(t) is in addition corrupted by noise. The usual linear methods for such inverse problems, for example those bas...

The article is devoted to the study of a possibility of on-line signature verification using the wavelet transform with the radial basis function. Representation of the signature in the form of function, invariant concerning a position, – the signature is replaced by a broken curve and is described using the angles between the adjacent links – is offered. Using the wavelet transforms for the si...

The wavelet transform is a comparatively new and fast developing method for analysing signals. The main advantage of applying the wavelet transform to the detection of edges in an image is the possibility of choosing the size of the details that will be detected. The size of detected edges is set by the wavelet scale. In the case of the discrete wavelet transform the choice of the scale is perf...

In this paper, we propose a hybrid video coder using the wavelet packet transform and motion compensation. To reduce the computational complexity of the wavelet packet decomposition, a novel criterion based on the rate-distortion function is proposed. After the wavelet packet transform, the successive quantization scheme and the adaptive arithmetic coder are applied for lossy wavelet coe cient ...

Issue of finding a wavelet matched to signal has been addressed by various researchers in past. This paper presents a new method of estimating wavelet that is matched to a given signal in the statistical sense. The key idea lies in the estimation of analysis wavelet filter from a given signal and is similar to a sharpening filter used in image enhancement. The output of analysis wavelet filter ...

Based on wavelet packet decomposition and conditions of the support vector kernel function, a nonlinear wavelet basis is introduced to construct the kernel function of support vector machine (SVM). A tighten wavelet support vector machine (WSVM), which has strong generalization ability is also obtained. In this study, a novel damage classification method based on wavelet support vector machine ...