相关论文: The Hyperanalytic Wavelet Transform

A trial wave function is proposed for studying the instability of the two-dimensional Hubbard model with respect to d-wave superconductivity. Double occupancy is reduced in a similar way as in previous variational studies, but in addition…

Some connections between operator theory and wavelet analysis: Since the mid eighties, it has become clear that key tools in wavelet analysis rely crucially on operator theory. While isolated variations of wavelets, and wavelet…

This paper develops new theory and algorithms for 1D general mode decompositions. First, we introduce the 1D synchrosqueezed wave packet transform and prove that it is able to estimate the instantaneous information of well-separated modes…

This paper has three main contributions. The first is the construction of wavelet transforms from B-spline scaling functions defined on a grid of non-equispaced knots. The new construction extends the equispaced, biorthogonal, compactly…

In the present work the well known Farey map is exploited to consruct a new mother wavelet. Properties such as admissibility, moments, 2-scale relation and reconstruction rule have been established. The constructed mother may be a good…

Wave motion in two- and three-dimensional periodic lattices of beam members supporting longitudinal and flexural waves is considered. An analytic method for solving the Bloch wave spectrum is developed, characterized by a generalized…

We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…

Typical LHC analyses search for local features in kinematic distributions. Assumptions about anomalous patterns limit them to a relatively narrow subset of possible signals. Wavelets extract information from an entire distribution and…

In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are - unlike more traditional transforms like wavelets -…

Inspired by recent interest in geometric deep learning, this work generalises the recently developed Slepian scale-discretised wavelets on the sphere to Riemannian manifolds. Through the sifting convolution, one may define translations and,…

We present the application of variational-wavelet analysis to numerical/analytical calculations of Wigner functions in (nonlinear) quasiclassical beam dynamics problems. (Naive) deformation quantization and multiresolution representations…

This report aims to present my research updates on distance function wavelets (DFW) based on the fundamental solutions and the general solutions of the Helmholtz, modified Helmholtz, and convection-diffusion equations, which include the…

Discrete wavelet-based methods promise to emerge as an excellent framework for the non-perturbative analysis of quantum field theories. In this work, we investigate aspects of renormalization in theories analyzed using wavelet-based…

Generating highly detailed, complex data is a long-standing and frequently considered problem in the machine learning field. However, developing detail-aware generators remains an challenging and open problem. Generative adversarial…

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from…

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…

We consider the 1D Tonks-Girardeau gas with a space-dependent potential out of equilibrium. We derive the exact dynamics of the system when divided into $n$ boxes and decomposed into energy eigenstates within each box. It is a…

The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…

We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented structure in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal…

Variational Autoencoders (VAEs) are powerful generative models capable of learning compact latent representations. However, conventional VAEs often generate relatively blurry images due to their assumption of an isotropic Gaussian latent…