Related papers: Composite Wavelet Transforms: Applications and Per…
In frame theory literature, there are several generalizations of frame, K-fusion frame presents a flavour of one such generalization, basically it is an intertwined replica of K-frame and fusion frame. K-fusion frames come naturally (having…
In this paper, we show how a class of operators used in the analysis of measures from wavelets and iterated function systems may be understood from a special family of representations of Cuntz algebras.
Compressed sensing (CS) using overcomplete wavelet dictionaries has been a well-investigated topic in the recent times for image and vision applications. In this paper, different overcomplete wavelet transforms have been studied to estimate…
We consider a class of semidirect products $G = \mathbb{R}^n \rtimes H$, with $H$ a suitably chosen abelian matrix group. The choice of $H$ ensures that there is a wavelet inversion formula, and we are looking for criteria to decide under…
We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…
New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible $\zed$-valued…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
In this paper we consider the kernel of the radially deformed Fourier transform introduced in the context of Clifford analysis in [10]. By adapting the Laplace transform method from [4], we obtain the Laplace domain expressions of the…
The inverse Radon transform allows to obtain partonic double distributions from (extended) generalized parton distributions. We express the extension of generalized parton distributions by their dual parts, generalized distribution…
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the…
This paper examines the wavelet multiplicity function. An explicit formula for the multiplicity function is derived. An application to operator interpolation is then presented. We conclude with several remarks regarding the wavelet…
In this paper, we consider the design of wavelet filters based on the Thiran common-factor approach proposed in Selesnick [2001]. This approach aims at building finite impulseresponse filters of a Hilbert-pair of wavelets serving as real…
We construct a Continuous Wavelet Transform (CWT) on the torus $\mathbb T^2$ following a group-theoretical approach based on the conformal group $SO(2,2)$. The Euclidean limit reproduces wavelets on the plane $\mathbb R^2$ with two…
The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind. The result is the exact analytical representation as the series of the Bessel and Struve functions multiplied by the…
We present the first wavelet-based all-electron density-functional calculations to include gradient corrections and the first in a solid. Direct comparison shows this approach to be unique in providing systematic ``transparent''…
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure.…
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…
Using the notions of frame transform and of square integrable projective representation of a locally compact group $G$, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier…