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The article deals with a classical inverse problem: the computation of the refractive index of a medium from ultrasound time-of-flight (TOF) measurements. This problem is very popular in seismics but also for tomographic problems in…
This article is concerned with tensor field tomography in a fairly general setting, that takes refraction, attenuation and time-dependence of tensor fields into account. The mathematical model is given by attenuated ray transforms of the…
We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative…
We use the transfer equation in relativistic form to develop an expansion of the one-photon distribution for a medium with constant photon mean free path, $\epsilon$. The resulting radiative viscosity tensor may be expressed either as a…
We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…
We consider a time-independent variable coefficients fractional porous medium equation and formulate an associated inverse problem. We determine both the conductivity and the absorption coefficient from exterior partial measurements of the…
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
We extend the study of inverse boundary value problems to the setting of fully nonlinear PDEs by considering an inverse source problem for the Monge-Amp\`ere equation \[ \det D^2 u = F. \] We prove that, on a convex Euclidean domain in the…
This article proposes a process to reconstruct a Riemann surface with boundary equipped with a conductivity tensor from its boundary and its Dirichlet-Neumann operator. When initial data comes from a two dimensional real Riemannian oriented…
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluorophores in biological tissue by the one single boundary…
In this paper we develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular,…
Many naturally-occuring models in the sciences are well-approximated by simplified models, using multiscale techniques. In such settings it is natural to ask about the relationship between inverse problems defined by the original problem…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to recover the slowness field of a medium based on the boundary…
Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge of transport maps offers a mathematical foundation and new insights for tackling this challenge by…
An approach to diffraction tomography is investigated for two-dimensional image reconstruction of objects surrounded by an arbitrarily-shaped curve of sources and receivers. Based on the integral theorem of Helmholtz and Kirchhoff, the…
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…