Related papers: The Radon Transform-Based Sampling Methods for Bih…
Estimation of the number of sources in a linear mixture is a critical preprocessing step in the separation and analysis of the sources for many applications. Historically, statistical methods, such as the minimum description length and…
In three dimensional scattering, the energy continuum wavefunction is obtained by utilizing two independent solutions of the reference wave equation. One of them is typically singular (usually, near the origin of configuration space). Both…
This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhomogeneous background medium. For convex-polygonal source…
An interpolation method to evaluate magnetic fields given unstructured, scattered magnetic data is presented. The method is based on the reconstruction of the global magnetic field using a superposition of orthogonal functions. The…
We describe the method used to detect sources for the Herschel-ATLAS survey. The method is to filter the individual bands using a matched filter, based on the point-spread function (PSF) and confusion noise, and then form the inverse…
In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
The problem studied in this paper is ultrasound image reconstruction from frequency-domain measurements of the scattered field from an object with contrast in attenuation and sound speed. The case where the object has uniform but unknown…
Researchers routinely characterize optical samples by computing the scattering cross-section. However, the experimental determination of this magnitude requires the measurement and integration of the components of the scattered field in all…
This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…
In this paper, we extend the resonant modal theory (RMT) developed previously for a metal object to an arbitrary source region consisting of metals, dielectrics, or the combination of both. The influences of dielectrics on the fields are…
In this paper, we develop a two-stage distributed algorithm that enables nodes in a graph to cooperatively estimate the spectrum of a matrix $W$ associated with the graph, which includes the adjacency and Laplacian matrices as special…
This paper is concerned with inverse scattering problems of determining the support of an isotropic and homogeneous penetrable body from knowledge of multi-static far-field patterns in acoustics and in linear elasticity. The normal…
We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scatterers. The theoretical justification of our novel sampling…
The advent of high density 3D wide azimuth survey configurations has greatly increased the cost of seismic acquisition. Simultaneous source acquisition presents an opportunity to decrease costs by reducing the survey time. Source time…
Significant challenges exist in efficient data analysis of most advanced experimental and observational techniques because the collected signals often include unwanted contributions--such as background and signal distortions--that can…
We propose a universal approach for modeling complex integrated photonic resonators based on the scattering matrix method. By dividing devices into basic elements including directional cou-plers and connecting waveguides, our approach can…
In medical SPECT imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first order scattering measurements. The problem is modeled using the…
The inverse problem of reconstructing a source term from boundary measurements, for the wave equation, is revisited. We propose a novel approach to recover the unknown source through measuring the wave fields after injecting small…
This paper investigates inverse source problems for time-dependent electromagnetic waves governed by Maxwell's equations. After applying the Fourier transform with respect to time, the problem leads to a frequency-domain electromagnetic…