Related papers: A Method for Constructing Wavelet Functions on the…
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 recent years it has turned out that shearlets have the potential to retrieve directional information so that they became interesting for many applications. Moreover the continuous shearlet transform has the outstanding property to stem…
Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical…
(Abridged) Wavelet analysis can be used to measure the power spectrum of solar wind fluctuations along a line in any direction with respect to the local mean magnetic field. This technique is applied to study solar wind turbulence in…
In this paper, we consider the sparse regularization of manifold-valued data with respect to an interpolatory wavelet/multiscale transform. We propose and study variational models for this task and provide results on their well-posedness.…
This paper presents a wavelet representation using baseband signals, by exploiting Kotel'nikov results. Details of how to obtain the processes of envelope and phase at low frequency are shown. The archetypal interpretation of wavelets as an…
In this paper high resolution wave probe records are examined using wavelet techniques with a view to determining the sources and relative contributions of capillary wave energy along representative wind wave forms. Wavelets enable…
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…
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…
Federated learning (FL) is a collaborative machine learning paradigm, which enables deep learning model training over a large volume of decentralized data residing in mobile devices without accessing clients' private data. Driven by the…
For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on…
Wavelet set wavelets were the first examples of wavelets that may not have associated multiresolution analyses. Furthermore, they provided examples of complete orthonormal wavelet systems in $L^2(\mathbb{R}^d)$ which only require a single…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet.…
This paper addresses the problem of regularity properties of functions represented as an expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov norm with probability 1. Such representations are used to…
Automatic generation of sequences has been a highly explored field in the last years. In particular, natural language processing and automatic music composition have gained importance due to the recent advances in machine learning and…
It is challenging for full-waveform inversion to determine geologically informative models from field data. An inaccurate wavelet can make it more complicated. We develop a novel misfit function, entitled deconvolutional double-difference…
In this paper, we design mother wavelets for the 1D continuous wavelet transform with some optimality properties. An optimal mother wavelet here is one that has an ambiguity function with minimal spread in the continuous coefficient space…
Choose a random degree d poly f with coefficients in a finite field F. We estimate the ultimate period of f under compositional iteration. We also determine the joint distribution of the small cycle lengths in the graph with edges (x,f(x)),…
Large scale real number computation is an essential ingredient in several modern mathematical proofs. Because such lengthy computations cannot be verified by hand, some mathematicians want to use software proof assistants to verify the…