Related papers: A directional continuous wavelet transform on the …
New orthonormal basis of eigenfunctions for the Vladimirov operator of p-adic fractional derivation is constructed. The map of p-adic numbers onto real numbers (p-adic change of variables) is considered. This map (for p=2) provides an…
Many real-life signals are defined on spherical domains, in particular in geophysics and physics applications. In this work, we tackle the problem of extending the iterative filtering algorithm, developed for the decomposition of…
A multiresolution analysis for a Hilbert space realizes the Hilbert space as the direct limit of an increasing sequence of closed subspaces. In a previous paper, we showed how, conversely, direct limits could be used to construct Hilbert…
Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…
In this paper, we study nonhomogeneous wavelet systems which have close relations to the fast wavelet transform and homogeneous wavelet systems. We introduce and characterize a pair of frequency-based nonhomogeneous dual wavelet frames in…
There is constructed and considered the extension of classical Diriclet operator corresponding to uniformly log-concave measure in the space of symmetric differential forms. Sufficient conditions for its essential self-adjointness in…
We address the question of designing isotropic analysis functions on the sphere which are perfectly limited in the spectral domain and optimally localized in the spatial domain. This work is motivated by the need of localized analysis tools…
We describe local and global properties of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand-Shilov type spaces and their duals. In…
Wavelets are widely used in various disciplines to analyse signals both in space and scale. Whilst many fields measure data on manifolds (i.e., the sphere), often data are only observed on a partial region of the manifold. Wavelets are a…
Like the continous shearlet transform and their relatives, discrete transformations based on the interplay between several filterbanks with anisotropic dilations provide a high potential to recover directed features in two and more…
A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L…
This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet type and may be defined on sets of arbitrarily distributed data…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…
We introduce a general framework for the construction of polynomial frames in $L^2(\mathbb{S}^{d-1})$, $d \geq 3$, where the frame functions are obtained as rotated versions of an initial sequence of polynomials $\Psi^j$, $j\in…
This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general…
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 propose and study a new quasi-interpolation method on spheres featuring the following two-phase construction and analysis. In Phase I, we analyze and characterize a large family of zonal kernels (e.g., the spherical version of Poisson…
Small form-factor, narrowband, and highly directive antennas are of critical importance in a variety of applications spanning wireless communications, remote sensing, Raman spectroscopy, and single photon emission enhancement. Surprisingly,…
Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed…