Related papers: Empirical wavelet frames
Random Wavelet Series form a class of random processes with multifractal properties. We give three applications of this construction. First, we synthesize a random function having any given spectrum of singularities satisfying some…
We provide a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi affine frames. This result generalizes the characterization of wavelets on Euclidean spaces by means of two basic…
Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension such that they exhibit vanishing moments with respect to any prescribed set of…
Volumetric maps are widely used in robotics due to their desirable properties in applications such as path planning, exploration, and manipulation. Constant advances in mapping technologies are needed to keep up with the improvements in…
Recent results from real algebraic geometry and the theory of polynomial optimization are related in a new framework to the existence question of multivariate tight wavelet frames whose generators have at least one vanishing moment. Namely,…
Synthetic turbulence models are a useful tool that provide realistic representations of turbulence, necessary to test theoretical results, to serve as background fields in some numerical simulations, and to test analysis tools. Models of 1D…
The dielectric layers surrounding a metasurface have a large impact on its frequency and angular response. The notion of effective permittivity captures this dependence by suggesting that a layered dielectric environment will perturb…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
In the paper we design a Parseval wavelet frame with a compact support and many vanishing moments. The corresponding refinement mask approximates an arbitrary continuous periodic function $f$, $f(0)=1$. The refinable function has stable…
Evolutionary algorithms offer great promise for the automatic design of robot bodies, tailoring them to specific environments or tasks. Most research is done on simplified models or virtual robots in physics simulators, which do not capture…
Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…
A framework for virtual reality of engineering objects has been developed. This framework may simulate different equipment related to virtual reality. Framework supports 6D dynamics, ordinary differential equations, finite formulas, vector…
In the last decade, methods based on various kinds of spherical wavelet bases have found applications in virtually all areas where analysis of spherical data is required, including cosmology, weather prediction, and geodesy. In particular,…
It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet…
We investigate here a generalized construction of spherical wavelets/needlets which admits extra-flexibility in the harmonic domain, i.e., it allows the corresponding support in multipole (frequency) space to vary in more general forms than…
We explore the feasibility of foundation models for the simulation of physical phenomena, with emphasis on continuum (solid and fluid) mechanics. Although so-called learned simulators have shown some success when applied to specific tasks,…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This…
In this article, we follow closely the approach in Hernandez and Weiss's seminal text in describing the construction of an orthonormal wavelet from a multi-resolution analysis. We assume the reader has a modest background in analysis and…
Extending the concept of frame to continuous frame, in this manuscript we will show that under certain conditions on the measure of $\Omega$ and the dimension of $\h$ we can construct continuous frames. Also, some examples are given.