Related papers: A Method for Constructing Wavelet Functions on the…
In this paper we establish a multiscale approximation for random fields on the sphere using spherical needlets --- a class of spherical wavelets. We prove that the semidiscrete needlet decomposition converges in mean and pointwise senses…
While working within the spatial domain can pose problems associated with ill-conditioned scores caused by power-law decay, recent advances in diffusion-based generative models have shown that transitioning to the wavelet domain offers a…
In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
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.
Despite the eminent successes of deep neural networks, many architectures are often hard to transfer to irregularly-sampled and asynchronous time series that commonly occur in real-world datasets, especially in healthcare applications. This…
A function from sequences to their subsequences is called selection function. A selection function is called admissible (with respect to normal numbers) if for all normal numbers, their subsequences obtained by the selection function are…
Collective variable-based enhanced sampling methods are routinely used on systems with metastable states, where high free energy barriers impede proper sampling of the free energy landscapes when using conventional molecular dynamics…
Aperture array interferometers, such as that proposed for the Square Kilometre Array (SKA), will see the entire sky, hence the standard approach to simulating visibilities will not be applicable since it relies on a tangent plane…
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…
Let $q\geq 2$ be an integer, and $\Bbb F_q^d$, $d\geq 1$, be the vector space over the cyclic space $\Bbb F_q$. The purpose of this paper is two-fold. First, we obtain sufficient conditions on $E \subset \Bbb F_q^d$ such that the inverse…
We revisit the feasibility approach to the construction of compactly supported smooth orthogonal wavelets on the line. We highlight its flexibility and illustrate how symmetry and cardinality properties are easily embedded in the design…
Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing…
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 a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological…
In the present work, the notion of Super Fractal Interpolation Function (SFIF) is introduced for finer simulation of the objects of the nature or outcomes of scientific experiments that reveal one or more structures embedded in to another.…
Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…
The adjoint method is a popular method used for seismic (full-waveform) inversion today. The method is considered to give more realistic and detailed images of the interior of the Earth by the use of more realistic physics. It relies on the…
In this paper, we consider signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency…
We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element Method (WEMsFEM) motivated by \cite{MR3980476,GL18} to solve the singularly perturbed convection-diffusion equations. The main idea is to first establish a…