Related papers: Simultaneous source and attenuation reconstruction…
The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic…
The inverse scattering problem, whose goal is to reconstruct an unknown scattering object from its scattered wave, is essential in fundamental wave physics and its wide applications in imaging sciences. However, it remains challenging 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 present a cost-effective method for model calibration and solution of source inversion problems in atmospheric dispersion modelling. We use Gaussian process emulations of atmospheric dispersion models within a Bayesian framework for…
In this paper we consider the inverse problem of vibro-acoustography, a technique for enhancing ultrasound imaging by making use of nonlinear effects. It amounts to determining two spatially variable coefficients in a system of PDEs…
We propose in this paper a globally numerical method to solve a phaseless coefficient inverse problem: how to reconstruct the spatially distributed refractive index of scatterers from the intensity (modulus square) of the full complex…
In this paper, a new inversion model for 2D microwave imaging is introduced by means of a convenient rewriting of the usual Lippmann Schwinger integral scattering equation. Such model is derived by decomposing the Greens function and the…
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…
The present paper generalizes preceding papers of the author and opens a cycle of works concerning the general posing and solution in analytic form of the quantum-mechanical inverse scattering problem (for a given partial channel) in a…
We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded in the continuous spectrum. (3)Limiting…
Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the…
Imaging reconstruction of interferometric data is a hard ill-posed inverse problem. Its difficulty is increased when observing the Galactic Center, which is obscured by a scattering screen. This is because the scattering breaks the…
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…
We show that an inverse scattering problem for a semilinear wave equation can be solved on a manifold having an asymptotically Minkowskian infinity, that is, scattering functionals determine the topology, differentiable structure, and the…
In the previous paper "Stabilizing Inverse Problems by Internal Data", the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid)…
While it is well known that X-ray tomography using a polychromatic source is non-linear, as the linear attenuation coefficient depends on the wavelength of the X-rays, tomography using near monochromatic sources are usually assumed to be a…
We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The even-parity equations are solved using a diffusion…
Polarized NLTE radiative transfer in the presence of scattering in spectral lines and/or in continua may be cast in a so-called reduced form for six reduced components of the radiation field. In this formalism the six components of the…
The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total…
Inverse scattering methods capable of compressive imaging are proposed and analyzed. The methods employ randomly and repeatedly (multiple-shot) the single-input-single-output (SISO) measurements in which the probe frequencies, the incident…