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Crystalline defects critically influence material properties, necessitating accurate simulation methods. Existing approaches, from atomic-scale configurations to continuum elasticity, face inherent limitations in modeling…
Here we present exact, stationary, parametric solutions to the Schr\"odinger--Poisson system. We confront two images: on one hand, we draw on the homotopy analysis method which leads us to a nonlinear integral scheme. Indeed, this approach…
Tailoring spectral properties of photon pairs is of great importance for optical quantum information and measurement applications. High-resolution spectral measurement is a key technique for engineering spectral properties of photons,…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
Broadband precision spectroscopy is indispensable for providing high fidelity molecular parameters for spectroscopic databases. We have recently shown that mechanical Fourier transform spectrometers based on optical frequency combs can…
We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales,…
This paper introduces a novel technique to preserve spectral features in lossy compression based on a novel fast Fourier correction algorithm\added{ for regular-grid data}. Preserving both spatial and frequency representations of data is…
Optical spectroscopy plays an essential role across scientific research and industry for non-contact materials analysis1-3, increasingly through in-situ or portable platforms4-6. However, when considering low-light-level applications,…
Computational techniques have gained significant traction in photonics, enabling the co-design of hardware and data processing algorithms to drastically simplify optical system architectures and improve their performance. However, their…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
When light passes through a multimode fiber, two-dimensional random intensity patterns are formed due to the complex interference within the fiber. The extreme sensitivity of speckle patterns to the frequency of light paved the way for…
'The spectral leakage from windowing and the picket fence effect from discretization' have been among the standard contents in textbooks for many decades. The spectral leakage and picket fence effect would cause the distortions in…
We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…
Signal decomposition is an effective tool to assist the identification of modal information in time-domain signals. Two signal decomposition methods, including the empirical wavelet transform (EWT) and Fourier decomposition method (FDM),…
We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since…
We present measurements of the complete spatio-temporal Fourier spectrum of Faraday waves. The Faraday waves are generated at the interface of two immiscible index matched liquids of different density. By use of a new absorption technique…
Diffusion models have been shown to implicitly generate visual content autoregressively in the frequency domain, where low-frequency components are generated earlier in the denoising process while high-frequency details emerge only in later…
We demonstrate an optical frequency analysis method using the Fourier transform of detection times of fluorescence photons emitted from a single trapped 40Ca+ ion. The response of the detected photon rate to the relative laser frequency…
We introduce the Deep Spectral Prior (DSP), a new framework for unsupervised image reconstruction that operates entirely in the complex frequency domain. Unlike the Deep Image Prior (DIP), which optimises pixel-level errors and is highly…
This article addresses the problem of two- and higher dimensional pattern matching, i.e. the identification of instances of a template within a larger signal space, which is a form of registration. Unlike traditional correlation, we aim at…