Related papers: Symplectic-dilation mixed wavelet transform and it…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
We study the optical properties of hydrogen passivated silicon, germanium and mixed Ge/Si core/shell quantum dots (QDs) using high accuracy Density Functional Theory (DFT) and time-dependent DFT (TDFT). We employ the hybrid DFT functional…
The interaction of light with objects and media moving at relativistic and superluminal speeds enables unconventional phenomena such as Fresnel drag, Hawking radiation, and light amplification. Synthetic motion, facilitated by modulated…
Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special…
A non-decimated wavelet transform (NDWT) is a popular version of wavelet transforms because of its many advantages in applications. The inherent redundancy of this transform proved beneficial in tasks of signal denoising and scaling…
A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…
We show that the Fourier transform of the Deeply Virtual Compton Scattering (DVCS) amplitude with respect to the skewness variable $\zeta$ at fixed invariant momentum transfer squared $t$ provides a unique way to visualize the structure of…
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
The development of new techniques for characterizing atmospheric optical turbulence (OT) has become an active topic of research again in recent years. In order to facilitate these studies, we reconsidered known theoretical results and…
The theory of surface electromagnetic waves (SEMWs) propagating at optical frequencies along the interface of an isotropic noble metal [e.g., gold (Au)] and a uniaxial crystal [e.g., Rutile (TiO$_2$)] is revisited with the Drude-Lorentz…
Many real-world relational systems, such as social networks and biological systems, contain dynamic interactions. When learning dynamic graph representation, it is essential to employ sequential temporal information and geometric structure.…
A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…
The quantum Fourier transform (QFT), a quantum analog of the classical Fourier transform, has been shown to be a powerful tool in developing quantum algorithms. However, in classical computing there is another class of unitary transforms,…
Nonlinear optics of structured light has recently delivered intriguing fundamental physical phenomena in light-matter interactions and advanced applications from classical imaging to quantum informatics. The mutual interaction between spin,…
Upcoming LCLS-II/II-HE operation at repetition rates approaching 1MHz demands on-detector data reduction to manage the resulting data volumes. We present a 2D discrete wavelet transform (DWT) pre-processing algorithm that segments…
Recent advances in the chirplet transform and wavelet-chirplet transform (WCT) have enabled the estimation of instantaneous frequencies (IFs) and chirprates, as well as mode retrieval from multicomponent signals with crossover IF curves.…
Existing sequence to sequence models for structured language tasks rely heavily on the dot product self attention mechanism, which incurs quadratic complexity in both computation and memory for input length N. We introduce the Graph Wavelet…
In this letter, the wavelet transform is used to decompose the classical linearly polarized plane light wave into a series of discrete Morlet wavelets. It is found that the energy of the light wave can be discrete, associated with its…
This paper presents a novel Diffusion-Wavelet (DiWa) approach for Single-Image Super-Resolution (SISR). It leverages the strengths of Denoising Diffusion Probabilistic Models (DDPMs) and Discrete Wavelet Transformation (DWT). By enabling…