Related papers: Multiwave imaging in an enclosure with variable wa…
We describe a method for recovering the irradiance underlying a collection of images corrupted by atmospheric turbulence. Since supervised data is often technically impossible to obtain, assumptions and biases have to be imposed to solve…
In photoacoustic imaging the objective is to determine the optical properties of biological tissue from boundary measurement of the generated acoustic wave. Here, we propose a restriction to piecewise constant media parameters. Precisely we…
In this paper, we investigate the stability of the linear wave equation where one part of the boundary, which is seen as a lower-dimensional Riemannian manifold, is governed by a coupled wave equation, while the other part is subject to a…
The wave equation is time-reversal invariant. The enclosure method using a Neumann data generated by this invariance is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown…
We present a non-iterative algorithm to reconstruct the isotropic acoustic wave speed from the measurement of the Neumann-to-Dirichlet map. The algorithm is designed based on the boundary control method and involves only computations that…
We investigate the inverse problem of numerically identifying unknown initial temperatures in a heat equation with dynamic boundary conditions whenever some overdetermination data is provided after a final time. This is a backward parabolic…
The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and regularization. We present a model in frequency domain, prove…
This paper is concerned with a practical inverse problem of simultaneously reconstructing the surface heat flux and the thickness of a solid structure from the associated ultrasonic measurements. In a thermoacoustic coupling model, the…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…
In this article we are concerned with an inverse initial boundary value problem for a non-linear wave equation in space dimension $n\geq 2$. In particular we consider the so called interior determination problem. This non-linear wave…
We study the unique recovery of time-independent lower order terms appearing in the symmetric first order perturbation of the Riemannian wave equation by sending and measuring waves in disjoint open sets of \textit{a priori} known closed…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Under the assumption of constant speed of sound we develop an…
We consider the inverse source problem arising in thermo- and photo-acoustic tomography. It consists in reconstructing the initial pressure from the boundary measurements of the acoustic wave. Our goal is to extend versatile time reversal…
In this paper, we consider two types of damped wave equations: the weakly damped equation and the strongly damped equation. We recover the initial velocity from the trace of the solution on a space-time cylinder. This inverse problem is…
The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
In this paper, we investigate the recovery of the absorption coefficient from boundary data assuming that the region of interest is illuminated at an initial time. We consider a sufficiently strong and isotropic, but otherwise unknown…
The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…