Related papers: A Wavelet Plancherel Theory with Application to Mu…
Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields. In this survey we present several extensions of the Shannon…
It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters…
We introduce graph wedgelets - a tool for data compression on graphs based on the representation of signals by piecewise constant functions on adaptively generated binary graph partitionings. The adaptivity of the partitionings, a key…
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…
Very recently, Window-based Transformers, which computed self-attention within non-overlapping local windows, demonstrated promising results on image classification, semantic segmentation, and object detection. However, less study has been…
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…
Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features…
The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…
Group invariants are used in high energy physics to define quantum field theory interactions. In this paper, we are presenting the parallel algebraic computation of special invariants called symplectic and even focusing on one particular…
Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…
As a generalization of orthonormal wavelets in $L_2(R)$, tight framelets (also called tight wavelet frames) are of importance in wavelet analysis and applied sciences due to their many desirable properties in applications such as image…
Neural operators have gained recognition as potent tools for learning solutions of a family of partial differential equations. The state-of-the-art neural operators excel at approximating the functional relationship between input functions…
We investigate compactness and spectral properties of multiplier operators associated with the Walsh system in the spaces $L^p[0,1]$, $1<p<\infty$. Building upon previously established criteria for boundedness of Walsh multipliers, we prove…
We represent a bilinear Calder\'on-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in a…
A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth…
This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vall\'ee Poussin (VP) interpolation at Chebyshev nodes. Unlike classical wavelets, which…
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…
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…