This paper aims to study the q-wavelet and the q-wavelet transforms, associated with the q-Bessel operator for a fix q ∈]0, 1[. As application, an inversion formulas of the q-Riemann-Liouville and q-Weyl transforms using q-wavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their q-analogues.

We discuss the use of orthogonal wavelet transforms in multivariate data analysis methods such as clustering and dimensionality reduction. Wavelet transforms allow us to introduce multiresolution approximation, and multiscale nonparametric regression or smoothing, in a natural and integrated way into the data analysis. Applications illustrate the powerfulness of this new perspective on data ana...

This correspondence investigates M -band wavelet packets and a generalized framework for the design and efficient utilization of multirate filter bank trees (FBTs). While the increased flexibility of M -band wavelet packets over the standard 2-band wavelet packets is desirable in many signal processing applications, the possibilities in time-frequency design using arbitrary filter bank cascades...

In this paper we present a comparative study on fusion of visual and thermal images using different wavelet transformations. Here, coefficients of discrete wavelet transforms from both visual and thermal images are computed separately and combined. Next, inverse discrete wavelet transformation is taken in order to obtain fused face image. Both Haar and Daubechies (db2) wavelet transforms have b...

Symmetric extension is explored as a means for constructing nonexpansive reversible integer-to-integer (ITI) wavelet transforms for finite-length signals. Two families of reversible ITI wavelet transforms are introduced, and their constituent transforms are shown to be compatible with symmetric extension. One of these families is then studied in detail, and several interesting results concernin...

In this paper we show that discrete affine wavelet transforms can provide a tool for the analysis and synthesis of standard feedforward neural networks. It is shown that wavelet frames for L2(IR) can be constructed based upon sigmoids. The spatia-spectral localization property of wavelets can be exploited in defining the topology and determining the weights of a feedforward network. Training a ...

Standard DWT (Discrete Wavelet Transform), being non-redundant, is a very powerful tool for many non-stationary Signal Processing applications, but it suffers from three major limitations; 1) shift sensitivity, 2) poor directionality, and 3) absence of phase information. To reduce these limitations, many researchers developed real-valued extensions to the standard DWT such as WP (Wavelet Packet...

Several algorithms are reviewed for computing various types of wavelet transforms: the Mallat algorithm, the “a trous” algorithm and their generalizations by Shensa. The goal is 1) to develop guidelines for implementing discrete and continuous wavelet transforms efficiently, 2) to compare the various algorithms obtained and give an idea of possible gains by providing operation counts. The compu...

In this paperthe eflcient implementation of different types of orthogonal wavelet transforms with respect to practical applications is discussed. Orthogonal singlewuvelet triinsfornis being based on one scaling function and one wavelet function are used for denosing of signals. Orthogonal multiwavelets are bused on several scaling filnctions and several wavelets. Since they allow properties lik...

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...