相关论文: Inverse transport and diffusion problems in photoa…

We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…

We derive a grey linear diffusion equation for photons with respect to inertial (or lab-frame) space and time, using asymptotic analysis in 1D planar geometry. The solution of the equation is the comoving radiation energy density. Our…

In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the…

Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…

We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…

We consider the ultrasound imaging problem governed by a nonlinear wave equation of Westervelt type with variable wave speed. We show that the coefficient of nonlinearity can be recovered uniquely from knowledge of the Dirichlet-to-Neumann…

We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes…

We analyze the optical pump-probe reflection and transmission coefficients when the photoinduced response depends nonlinearly on the incident pump intensity. Under these conditions, we expect the photoconductivity depth profile to change…

We investigate a hybrid inverse problem in fluorescence ultrasound modulated optical tomography (fUMOT) in the diffusive regime. We prove that the absorption coefficient of the fluorophores at the excitation frequency and the quantum…

Diffusion models have been widely studied as effective generative tools for solving inverse problems. The main ideas focus on performing the reverse sampling process conditioned on noisy measurements, using well-established numerical…

Standard photoacoustic tomography (PAT) provides data that consist of time-dependent signals governed by the wave equation, which are measured on an observation surface. In contrast, the measured data from the recently invented full-field…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

In this paper, we study transport features of a one-dimensional beam-plasma system in the presence of multiple resonances. As a model description of the general problem of a warm energetic particle beam, we assume $n$ cold supra-thermal…

Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method…

We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at the boundary of the medium encoded in the Dirichlet-to-Neumann…

In this paper, we consider the direct and inverse problem for isotropic scatterers with two conductive boundary conditions. First, we show the uniqueness for recovering the coefficients from the known far-field data at a fixed incident…

We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse…

The goal of this paper is to develop numerical methods computing a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse scattering theory. The problem is challenging since it is nonlinear,…

Photoacoustic tomography (PAT) is a novel and promising technology in hybrid medical imaging that involves generating acoustic waves in the object of interest by stimulating electromagnetic energy. The acoustic wave is measured outside the…

We demonstrate that the spatial resolution of images in optical tomography is not limited to the fundamental length scale of one transport mean free path. This result is facilitated by the introduction of novel corrections to the standard…