Related papers: Wavelet Design with Optimally Localized Ambiguity …
We present a novel generative modeling framework,Wavelet-Fourier-Diffusion, which adapts the diffusion paradigm to hybrid frequency representations in order to synthesize high-quality, high-fidelity images with improved spatial…
In this paper, we introduce the concept of a mother waveform to address key challenges in 5th generation (5G) and 6th generation (6G) networks, including spectral efficiency, backward compatibility, enhanced flexibility, and the integration…
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux…
We present here a simple construction of a wavelet system for the three-dimensional ball, which we label \emph{Radial 3D Needlets}. The construction envisages a data collection environment where an observer located at the centre of the ball…
Latent Diffusion Models (LDM), a subclass of diffusion models, mitigate the computational complexity of pixel-space diffusion by operating within a compressed latent space constructed by Variational Autoencoders (VAEs), demonstrating…
The construction of optimally localized Wannier functions (and Wannier functions in general) for a Chern insulator has been considered to be impossible owing to the fact that the second moment of such functions is generally infinite. In…
Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed…
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…
Classically, anisotropic surface wave tomography is treated as an optimisation problem where it proceeds through a linearised two-step approach. It involves the construction of 2D group or phase velocity maps for each considered period,…
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…
With the increasing growth of technology and the entrance into the digital age, we have to handle a vast amount of information every time which often presents difficulties. So, the digital information must be stored and retrieved in an…
Variational wave function ansatze are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte…
We develop an effective computational tool for simulating the scattering of 1D waves by a composite layer architected in an otherwise homogeneous medium. The layer is designed as the union of segments cut from various mother periodic media,…
In active sensing systems, waveforms with ambiguity functions (AFs) of low peak sidelobe levels (PSLs) across a time delay and Doppler frequency shift plane (delay-Doppler plane) of interest are desirable for reducing false alarms.…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
This paper introduces the synchrosqueezed curvelet transform as an optimal tool for 2D mode decomposition of wavefronts or banded wave-like components. The synchrosqueezed curvelet transform consists of a generalized curvelet transform with…
Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than…
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…
We summarise the construction of exact axisymmetric scale-discretised wavelets on the sphere and on the ball. The wavelet transform on the ball relies on a novel 3D harmonic transform called the Fourier-Laguerre transform which combines the…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…