相关论文: Correlation based passive imaging with a white noi…

We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we…

We present a novel algorithm for high resolution coherent imaging of sound sources in random scattering media using time resolved measurements of the acoustic pressure at an array of receivers. The sound waves travel a long distance between…

Given a compact Riemannian manifold $(M,g)$, Chazarain, H\"ormander, Duistermaat, and Guillemin study the half-wave trace $\operatorname{HWT}_{M,g}(\tau) \in \mathscr{S}'(\mathbb{R}_\tau)$. From the asymptotics of the half-wave trace as…

In partially linear models the dependence of the response y on (x^T,t) is modeled through the relationship y=\x^T \beta+g(t)+\epsilon where \epsilon is independent of (x^T,t). In this paper, estimators of \beta and g are constructed when…

We continue the analysis of models of spontaneous wave function collapse with stochastic dynamics driven by non-white Gaussian noise. We specialize to a model in which a classical "noise" field, with specified autocorrelator, is coupled to…

The power density spectrum of a light curve is often calculated as the average of a number of spectra derived on individual time intervals the light curve is divided into. This procedure implicitly assumes that each time interval is a…

Testing for white noise is a classical yet important problem in statistics, especially for diagnostic checks in time series modeling and linear regression. For high-dimensional time series in the sense that the dimension $p$ is large in…

Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…

We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…

We establish the existence and uniqueness of strong solutions to stochastic porous media equations driven by L\'{e}vy noise on a $\sigma$-finite measure space $(E,\mathcal{B}(E),\mu)$, and with the Laplacian replaced by a negative definite…

We consider an inverse problem for a hyperbolic partial differential equation on a compact Riemannian manifold. Assuming that $\Gamma_1$ and $\Gamma_2$ are two disjoint open subsets of the boundary of the manifold we define the restricted…

In the present paper which follows our previous paper ``Mathematical models for passive imaging I: general background'', we discuss the case of surface waves in a medium which is stratified near its boundary at some scale comparable to the…

Detecting stochastic background radiation of cosmological origin is an exciting possibility for current and future gravitational-wave (GW) detectors. However, distinguishing it from other stochastic processes, such as instrumental noise and…

We consider nonparametric statistical inference on a periodic interaction potential $W$ from noisy discrete space-time measurements of solutions $\rho=\rho_W$ of the nonlinear McKean-Vlasov equation, describing the probability density of…

Gravitational Wave (GW) data bring an exceptional avenue to test the underlying models of coalescing compact objects. In the regime of strong gravity and high curvature, they allow the exploration of minute deviations from the best-fit…

Passive sonar signals contain complex characteristics often arising from environmental noise, vessel machinery, and propagation effects. While convolutional neural networks (CNNs) perform well on passive sonar classification tasks, they can…

The collection of individually resolvable gravitational wave (GW) events makes up a tiny fraction of all GW signals which reach our detectors, while most lie below the confusion limit and go undetected. Like voices in a crowded room, the…

We consider the problem, where a camera is tasked with determining one of two hypotheses: first with an incoherently-radiating quasi-monochromatic point source and the second with two identical closely spaced point sources. We are given…

A periodically-uneven (in one horizontal direction) stress-free boundary covering a linear, isotropic, homogeneous, lossless solid half space is submitted to a vertically-propagating shear-horizontal plane, body wave. The rigorous theory of…

Tikhonov regularization is studied in the case of linear pseudodifferential operator as the forward map and additive white Gaussian noise as the measurement error. The measurement model for an unknown function $u(x)$ is \begin{eqnarray*}…