Related papers: An inverse medium problem using Stekloff eigenvalu…
This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad…
Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…
In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding…
This paper describes the spherical concave mirror method for measuring the index of refraction of transparent liquids. We derived the refractive index equation using Snell's law and the small-angle approximation. We also verified the…
This paper is concerned with inverse acoustic scattering problem of inferring the position and shape of a sound-soft obstacle from phaseless far-field data. We propose the Bayesian approach to recover sound-soft disks, line cracks and…
We study an inverse initial-density problem for a nonlinear diffusive coagulation--fragmentation equation with known coagulation and fragmentation kernels. The objective is to recover the unknown initial particle-size distribution on a…
We describe a "spatio-spectral" deconvolution algorithm for wide-band imaging in radio interferometry. In contrast with the existing multi-frequency reconstruction algorithms, the proposed method does not rely on a model of the…
In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photoacoustic or thermoacoustic tomography. We derive and analyze…
In this paper, we consider the inverse eigenvalue problem for the positive doubly stochastic matrices, which aims to construct a positive doubly stochastic matrix from the prescribed realizable spectral data. By using the real Schur…
In this paper, we present algorithms for reconstructing an unknown compact scatterer embedded in a random noisy background medium, given measurements of the scattered field and information about the background medium and the sound profile.…
We introduce a method for analyzing radio interferometry data which produces maps which are optimal in the Bayesian sense of maximum posterior probability density, given certain prior assumptions. It is similar to maximum entropy…
We consider the multi-frequency inverse source problem for the scalar Helmholtz equation in the plane. The goal is to reconstruct the source term in the equation from measurements of the solution on a surface outside the support of the…
The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running…
We revisit the classical problem of electromagnetic wave refraction from a lossless dielectric to a lossy conductor, where both media are considered to be non-magnetic, linear, isotropic and homogeneous. We derive the Fresnel coefficients…
This paper proposes a new and efficient numerical algorithm for recovering the damping coefficient from the spectrum of a damped wave operator, which is a classical Borg-Levinson inverse spectral problem. The algorithm is based on inverting…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…
The inverse source problem where an unknown source is to be identified from the knowledge of its radiated wave is studied. The focus is placed on the effect that multi-frequency data has on establishing uniqueness. In particular, it is…
We deal with the Cauchy problem for a perturbed wave equation in the half-plane with data given on a part of the space-time boundary. The equation in consideration describes a wave process in a laterally inhomogeneous medium. We propose a…
We revisit the inverse problem of reconstructing a spatially varying diffusion coefficient in stationary elliptic equations from boundary Cauchy data. From a theoretical perspective, we introduce a gradient-weighted modification of the…
We consider a time-dependent linear diffusion equation together with a related inverse boundary value problem. The aim of the inverse problem is to determine, based on observations on the boundary, the non-homogeneous diffusion coefficient…