Related papers: Nonhomogeneous Wavelet Systems in High Dimensions
Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generator with parabolic scaling, shearing, and translation…
By using an asymptotic analysis and numerical simulations, we derive and investigate a system of homogenized Maxwell's equations for conducting material sheets that are periodically arranged and embedded in a heterogeneous and anisotropic…
Single-wavelength interferometry achieves high resolution for smooth surfaces but struggles with rough, industrially relevant ones due to limited unambiguous measuring range and speckle effects. Multi-wavelength interferometry addresses…
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our…
Orthogonal wavelets, or wavelet frames, for L^2(R) are associated with quadrature mirror filters (QMF). The latter constitute a set of complex numbers which relate the dyadic scaling of functions on R to the Z-translates, and which satisfy…
Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…
This tutorial provides a joint theoretical and experimental overview of heterodyne wave mixing spectroscopy, focusing mainly on four-wave mixing (FWM). This powerful and versatile time-resolved nonlinear optical spectroscopy technique…
In this article, we construct discrete tight frames for $L^2(\mathbb{S}^{d-1})$, $d\geq3$, which consist of localized polynomial wavelets with adjustable degrees of directionality. In contrast to the well studied isotropic case, these…
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
Wavelets are scaleable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero. In addition to their use as source characterizers, wavelet functions are rapidly gaining currency within…
It is an open problem whether any pair of Bessel sequences with wavelet structure can be extended to a pair of dual frames by adding a pair of singly generated wavelet systems. We consider the particular case where the given wavelet systems…
A fully coupled network of Mackey-Glass generators is considered. Each generator is described by a limit equation for the Mackey-Glass equation. The right parts are represented by a relay function obtained when the exponent in the…
We find that the EPE evaluation metrics of RAFT-stereo converge inconsistently in the low and high frequency regions, resulting high frequency degradation (e.g., edges and thin objects) during the iterative process. The underlying reason…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…
Multiplicative cascades are often used to represent the structure of multiscaling variables in many physical systems, specially turbulent flows. In processes of this kind, these variables can be understood as the result of a successive…
Wavelet sets that are finite unions of convex sets are constructed in $\mathbb R^n$, $n\geq 2$, for dilation by any expansive matrix that has a power equal to a scalar times the identity and also has all singular values greater than $\sqrt…
Dispersionless bands -- \emph{flatbands} -- provide an excellent testbed for novel physical phases due to the fine-tuned character of flatband tight-binding Hamiltonians. The accompanying macroscopic degeneracy makes any perturbation…
In this paper we propose spectral tools based on non-decimated complex wavelet transforms implemented by their matrix formulation. This non-decimated complex wavelet spectra utilizes both real and imaginary parts of complex-valued wavelet…
The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet…