Related papers: Characterizations of Multiframelets on $\mathbb{Q}…
This paper produces various results on $p$-adic multiframelet. Multiframelet is a frame-like sequence generated by multiple functions along with wavelet structure. Various properties of multiframelet in $L^{2}(\mathbb{Q}_{p})$ have been…
Wavelet analysis has been extended to the $p$-adic line $\mathbb{Q}_p$. The $p$-adic wavelets are complex valued functions with compact support. As in the case of real wavelets, the construction of the basis functions is recursive,…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…
p-Adic wavelet transform is considered as a possible tool for the description of hierarchic quantum systems
Compared to scalar framelets, multiframelets have certain advantages, such as relatively smaller supports on generators, high vanishing moments, etc. The balancing property of multiframelets is very desired, as it reflects how efficient…
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…
The analysis of multivariate time series data is challenging due to the various frequencies of signal changes that can occur over both short and long terms. Furthermore, standard deep learning models are often unsuitable for such datasets,…
An original multiplex scheme is introduced, which is based on Mallat's multiresolution formulation of wavelet systems. This system is adaptable and its implementation is well matched to digital signal processors and computers. The approach…
Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets…
This paper presents a discussion on multiframelet set, multiwavelet set and set correspond to super wavelet on local fields of positive characteristic. We characterize Parseval multiframelet set and give equivalent conditions multiwavelet…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
The main goal of this paper is to develop the MRA theory along with wavelet theory in L2(Qp). Generalized scaling sets are important in wavelet theory because it determine multiwavelet sets. Although the theory of scaling set and…
We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction, tailored to the…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
In this paper, we study the convolution structure in the special affine Fourier domain to combine the advantages of the well known special affine Fourier and wavelet transforms into a novel integral transform coined as special affine…
Recently, the reference functions for the synthesis and analysis of the autostereoscopic multiview and integral images in three-dimensional displays we introduced. In the current paper, we propose the wavelets to analyze such images. The…
The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…
A multidimensional basis of p-adic wavelets is constructed. The relation of the constructed basis to a system of coherent states (i.e. orbit of action) for some $p$-adic group of linear transformations is discussed. We show that the set of…