Related papers: Some applications of the Tsirelson spectral measur…
In this paper, we propose to study spectral measures on local fields. Some basic results are presented, including the stability of Bessel sequences under perturbation, the Landau theorem on Beurling density, the law of pure type of spectral…
This article considers the application of particle filtering to continuous-discrete optimal filtering problems, where the system model is a stochastic differential equation, and noisy measurements of the system are obtained at discrete…
I discuss approaches to optimally remove noise from images. A generalization of Wiener filtering to Non-Gaussian distributions and wavelets is described, as well as an approach to measure the errors in the reconstructed images. We argue…
A Wiener filter can be interpreted as a cascade of a whitening- and an estimation filter. This paper gives a detailed investigates of the properties of these two filters. Then the practical consequences for the overall Wiener filter are…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
We treat the optimal linear filtering problem for a sum of two second order uncorrelated generalized stochastic processes. This is an operator equation involving covariance operators. We study both the wide-sense stationary case and the…
Reflection spectroscopy in the Near Infrared (NIR) is used to investigate the surface composition of Trans-Neptunian objects (TNOs). In general, these spectra are difficult to interpret due to the low apparent brightness of the TNOs,…
Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solution to this problem is governed by the so-called filtering…
Correlated noise sources, particularly magnetic noise, form a risk to future gravitational-wave searches aimed at detecting the gravitational-wave background. Potential noise contamination is investigated by making noise projections which…
The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…
A seismic array has been deployed at the Sanford Underground Research Facility in the former Homestake mine, South Dakota, to study the underground seismic environment. This includes exploring the advantages of constructing a…
The conventional Wien filter is a device with orthogonal static magnetic and electric fields, often used for velocity separation of charged particles. Here we describe the electromagnetic design calculations for a novel waveguide RF Wien…
We study the noise, in the sense of Tsirelson, generated by Harris flows. A criterion is given for the noise to be non-white, and in this case we study the associated spectral sets.
The variational formulation of nonlinear filtering due to Mitter and Newton characterizes the filtering distribution as the unique minimizer of a free energy functional involving the relative entropy with respect to the prior and an…
This work presents a unified framework for defining a family of noise reduction techniques for speech enhancement applications. The proposed approach provides a unique theoretical foundation for some widely-applied soft and hard…
The cancellation of noise from terrestrial gravity fluctuations, also known as Newtonian noise (NN), in gravitational-wave detectors is a formidable challenge. Gravity fluctuations result from density perturbations associated with…
In paper I (Yu et al. [1]), we show through N-body simulation that a local monotonic Gaussian transformation can significantly reduce non-Gaussianity in a noise-free lensing convergence field. This makes the Gaussianization a promising…
Ground-based gravitational-wave interferometers could directly probe the existence of ultralight dark matter ($\mathcal{O}(10^{-14}-10^{-11})$ eV/$c^2$) that couples to standard-model particles in the detectors. Recently, many techniques…
Synchronization of rotations is the problem of estimating a set of rotations R_i in SO(n), i = 1, ..., N, based on noisy measurements of relative rotations R_i R_j^T. This fundamental problem has found many recent applications, most…
We prove sharp estimates on the time-average behavior of the squared absolute value of the Fourier transform of some absolutely continuous measures that may have power-law singularities, in the sense that their Radon-Nikodym derivatives…