Related papers: Reconstructions for some coupled-physics inverse p…
The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded variation. The paper extends earlier results on smooth…
This paper concerns the reconstruction of a diffusion coefficient in an elliptic equation from knowledge of several power densities. The power density is the product of the diffusion coefficient with the square of the modulus of the…
The reconstruction task in photoacoustic tomography can vary a lot depending on measured targets, geometry, and especially the quantity we want to recover. Specifically, as the signal is generated due to the coupling of light and sound by…
This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…
We consider the numerical reconstruction of the spatially dependent conductivity coefficient and the source term in elliptic partial differential equations in a two-dimensional convex polygonal domain, with the homogeneous Dirichlet…
This paper aims to mathematically advance the field of quantitative thermo-acoustic imaging. Given several electromagnetic data sets, we establish for the first time an analytical formula for reconstructing the absorption coefficient from…
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…
Physical models often contain unknown functions and relations. In order to gain more insights into the nature of physical processes, these unknown functions have to be identified or reconstructed. Mathematically, we can formulate this…
In the context of model order reduction of parametric elliptic problems, we present a methodology to reconstruct a conforming flux from a given reduced solution, that is locally conservative with respect to the underlying finite element…
The aim of this paper is to tackle the nonlinear optical reconstruction problem. Given a set of acousto-optic measurements, we develop a mathematical framework for the reconstruction problem in the case where the optical absorption…
This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from…
Our goal is to reconstruct tomographic images with few measurements and a low signal-to-noise ratio. In clinical imaging, this helps to improve patient comfort and reduce radiation exposure. As quantum computing advances, we propose to use…
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving…
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…
Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
A multi-scale approach to the inverse reconstruction of a pattern's microstructure is reported. Instead of a correlation function, a pair of entropic descriptors (EDs) is proposed for stochastic optimization method. The first of them…
We propose a numerical algorithm for the reconstruction of a piecewise constant leading coefficient of an elliptic problem. The inverse problem is reduced to a shape reconstruction problem. The proposed algorithm is based on the…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…