Related papers: Quantifying uncertainty in inverse scattering prob…
We consider the scattering of time-harmonic plane waves by a compactly supported inhomogeneous scattering obstacle governed by the Helmholtz equation. Given far field observations of the scattered fields corresponding to plane wave incident…
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…
This paper is concerned with the inverse problem to recover a compactly supported Schr{\"o}dinger potential given the differential scattering cross section, i.e. the modulus, but not the phase of the scattering amplitude. To compensate for…
The concept of scattering coefficients has played a pivotal role in a broad range of inverse scattering and imaging problems in acoustic, and electromagnetic media. In view of their promising applications in inverse problems related to…
We propose an inverse-design approach for computational spectrometers in which the scattering media are topology-optimized to achieve better performance in inference of unknown spectra. Unlike traditional end-to-end approaches, our inverse…
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies.…
In the case of multi-parameter full-waveform inversion, the computation of the additional Hessian terms that contain derivatives with respect to more than one type of parameter is necessary. If a simple gradient-based minimization is used,…
This paper analyzes inverse scattering for the one-dimensional Helmholtz equation in the case where the wave speed is piecewise constant. Scattering data recorded for an arbitrarily small interval of frequencies is shown to determine the…
A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…
We consider an inverse boundary value problem for determining unknown scatterers, which is governed by the Helmholtz equation in a bounded domain. To address this, we develop a novel convex data-fitting formulation that is capable of…
The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm…
Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this paper, we consider reflection tomography of high contrast objects…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…
We consider the inverse problem of quantitative reconstruction of properties (e.g., bulk modulus, density) of visco-acoustic materials based on measurements of responding waves after stimulation of the medium. Numerical reconstruction is…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
Wave propagation and acoustic scattering problems require vast computational resources to be solved accurately at high frequencies. Asymptotic methods can make this cost potentially frequency independent by explicitly extracting the…
Accurate determination of the complex effective permittivity is fundamental to optical material engineering, but it remains a critical metrology challenge for heterogeneous systems. In polymer blends and optical composites, scattering and…
Interpreting scattered acoustic and electromagnetic wave patterns is a computational task that enables remote imaging in a number of important applications, including medical imaging, geophysical exploration, sonar and radar detection, and…
This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model…