相关论文: Uniqueness of two phaseless inverse acoustics prob…
In this article, we study the one-dimensional inverse problem of determining the memory kernel by the integral overdetermination condition for the direct problem of finding the velocity potential and the displacement of boundary points. A…
An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an…
An inverse problem of acoustic sounding is under consideration in a form of 3D inverse coefficient problem for wave equation. Unknown coefficient is the local propagation velocity of vibrations, which is associated with inhomogeneities of…
The fixed angle inverse scattering problem for a velocity consists in determining a sound speed, or a Riemannian metric up to diffeomorphism, from measurements obtained by probing the medium with a single plane wave. This is a formally…
Motivated by non-destructive testing of optical fiber, we consider the problem of determining the index of refraction of a two-dimensional medium from magnitude of the total field resulting from known incident plane waves at a fixed…
This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace…
In this paper, we study the photoacoustic tomography problem for which we seek to recover both the initial state of the pressure field and the wave speed of the medium from the knowledge of a single boundary measurement. The goal is to…
In this article, we investigate inverse source problems for a wide range of PDEs of parabolic and hyperbolic types as well as time-fractional evolution equations by partial interior observation. Restricting the source terms to the form of…
The phase retrieval problem has a long history and is an important problem in many areas of optics. Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered…
It is proved that the scattering amplitude $A(\beta, \alpha_0, k_0)$, known for all $\beta\in S^2$, where $S^2$ is the unit sphere in $\mathbb{R}^3$, and fixed $\alpha_0\in S^2$ and $k_0>0$, determines uniquely the surface $S$ of the…
We discuss direct and inverse spectral theory for the isospectral problem of the dispersionless Camassa--Holm equation, where the weight is allowed to be a finite signed measure. In particular, we prove that this weight is uniquely…
We prove that a sound-soft polyhedral scatterer is uniquely determined by the far-field pattern corresponding to an incident plane wave at one given wavenumber and one given incident direction.
The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering…
In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation,…
In this paper we prove uniqueness in the inverse boundary value problem for the three coefficient functions in the porous medium equation with an absorption term $\epsilon\partial_t u-\nabla\cdot(\gamma\nabla u^m)+\lambda u^q=0$, with…
We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…
An inverse scattering problem is analyzed for vowel articulation in the human vocal tract. When a unit amplitude, monochromatic, sinusoidal volume velocity is sent from the glottis towards the lips, various types of scattering data are used…
Sound scattering by a finite width beam on a single rigid body rotation vortex flow is detected by a linear array of transducers (both smaller than a flow cell), and analyzed using a revised scattering theory. Both the phase and amplitude…
We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely…
We study the inverse scattering problem for electric potentials and magnetic fields in $\ere^d, d\geq 3$, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from…