The projection method is a useful tool for analyzing various properties of multivariate refinable function vectors and for obtaining low-dimensional refinable function vectors and wavelets from high-dimensional ones. In this paper, we shall further study the projection method and its applications to multivariate wavelet and framelet systems. Examples will be given to illustrate the projection m...

In 2006, Saito and Remy presented a new algorithm called polyharmonic local sine transform (PHLST) in image processing as follows. Let f be a twice continuously differentiable function on a domain Ω. First we approximate f by a polyharmonic function u such that the residual component v = f −u vanishes in the boundary of Ω. Next, we do the odd extension for v, and then do the periodic extension,...

Well logging is an important tool for the characterization of subsurface rocks, being commonly used in the study of reservoir geology. It is well known that signals obtained as responses from geological media contain noise that can affect their interpretation, and that wavelet transform is more suitable than the Fourier transform to denoise non-stationary signals, as the ones obtained from well...

The de-noising of sensor data has become an important to research. Since the traditional de-noising method can’t achieve successful de-noising effect and the software-only method never meets a high real time capability. In this paper, we illustrate a novel threshold function based on the wavelet hard and soft threshold function. It is unlike ordinary function, which has overcome the defect such...

The purpose of this paper is a spectrum analysis signals various nature, construction the signal scalogram using Morlet wavelet, modification to obtain more informative graphic representation signal. Spectral constructed by means Fourier transform. A graphical result wavelet transform has been developed with help Mathematica system. For this, used as two-dimensional original scale introduced on...

‎this article presents a systematic study for structure of finite wavelet frames‎ ‎over prime fields‎. ‎let $p$ be a positive prime integer and $mathbb{w}_p$‎ ‎be the finite wavelet group over the prime field $mathbb{z}_p$‎. ‎we study theoretical frame aspects of finite wavelet systems generated by‎ ‎subgroups of the finite wavelet group $mathbb{w}_p$.

In the present paper, Wavelet Networks, are proven to be, as well as many other neural paradigms, a speci c case of the generic paradigm named Weighted Radial Basis Functions Networks. Moreover, a fair comparison between Wavelet and more traditional WRBF networks for function approximation is attempted, in order to demonstrate that the performance depends only on how good the chosen mother/acti...

Introduction: A major problem facing the patients with chronic liver diseases is the diagnostic procedure.  The conventional diagnostic method depends mainly on needle biopsy which is an invasive method. There  are  some  approaches  to  develop  a  reliable  noninvasive  method  of  evaluating  histological  changes  in  sonograms. The main characteristic used to distinguish between the normal...

In this paper nonparametric wavelet estimators of the quantile density function are proposed. Consistency of the wavelet estimators is established under the Lp risk. A simulation study illustrates the good performance of our estimators.

This paper presents a recursive method of modal parameters identification based on operational measurements, dedicated for non-stationary systems. Decoupling signal components procedure allowed to reduce the signal model and simplified the process of modal parameters estimation. Adaptive method of filtering simplified the process of wavelet function selection. Presented method utilize Continuou...