Related papers: Flaglets: Exact Wavelets on the Ball
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.
In this paper we show that the discrete Fourier transform can be performed by scattering a coherent particle or laser beam off a two-dimensional potential that has the shape of rings or peaks. After encoding the initial vector into the…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
In this article, we develop a general method for constructing wavelets {|det A_j|^{1/2} g(A_jx-x_{j,k}): j in J, k in K}, on irregular lattices of the form X={x_{j,k} in R^d: j in J, k in K}, and with an arbitrary countable family of…
We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…
Some recent methods, like the Empirical Mode Decomposition (EMD), propose to decompose a signal accordingly to its contained information. Even though its adaptability seems useful for many applications, the main issue with this approach is…
We give new formulas for finding a compactly supported function $v$ on $\mathbb{R}^d$, $d\geq 1$, from its Fourier transform $\mathcal{F} v$ given within the ball $B_r$. For the one-dimensional case, these formulas are based on the theory…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
It is demonstrated that the wavelets can be used to considerably speed up simulations of the wave packet propagation in multiscale systems. Extremely high efficiency is obtained in the representation of both bound and continuum states. The…
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…
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…
This paper describes a method for extracting rapidly varying, superimposed amplitude- and frequency-modulated signal components. The method is based upon the continuous wavelet transform (CWT) and uses a new wavelet which is a modification…
In this paper we aim to give various explicit and local estimates of ball prolate spheroidal wave functions defined in [25] as eigenfunctions of both finite Fourier transform and some differential operator. In particular, we give further…
In this paper we study how zeros of the Fourier transform of a function $f: \mathbb{Z}_p^d \to \mathbb{C}$ are related to the structure of the function itself. In particular, we introduce a notion of bandwidth of such functions and discuss…
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
Wave turbulence in a thin elastic plate is experimentally investigated. By using a Fourier transform profilometry technique, the deformation field of the plate surface is measured simultaneously in time and space. This enables us to compute…
We describe the construction of a spherical wavelet analysis through the inverse stereographic projection of the Euclidean planar wavelet framework, introduced originally by Antoine and Vandergheynst and developed further by Wiaux et al.…
This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and…