Inverse problems: seeing the unseen

G Uhlmann - Bulletin of Mathematical Sciences, 2014 - Springer
This survey article deals mainly with two inverse problems and the relation between them.
The first inverse problem we consider is whether one can determine the electrical …

[HTML][HTML] Mathematical and numerical challenges in diffuse optical tomography inverse problems

A Aspri, A Benfenati, P Causin… - … Dynamical Systems-S, 2024 - aimsciences.org
Computed Tomography (CT) is an essential imaging tool for medical inspection, diagnosis
and prevention. While X-rays CT is a consolidated technology, there is nowadays a strong …

The Calderón problem for the fractional Schrödinger equation with drift

M Cekić, YH Lin, A Rüland - Calculus of Variations and Partial Differential …, 2020 - Springer
We investigate the Calderón problem for the fractional Schrödinger equation with drift,
proving that the unknown drift and potential in a bounded domain can be determined …

A one-step reconstruction algorithm for quantitative photoacoustic imaging

T Ding, K Ren, S Vallélian - Inverse Problems, 2015 - iopscience.iop.org
Quantitative photoacoustic tomography (QPAT) is a recent hybrid imaging modality that
couples optical tomography with ultrasound imaging to achieve high resolution imaging of …

Quantitative photoacoustic imaging in radiative transport regime

AV Mamonov, K Ren - arxiv preprint arxiv:1207.4664, 2012 - arxiv.org
The objective of quantitative photoacoustic tomography (QPAT) is to reconstruct optical and
thermodynamic properties of heterogeneous media from data of absorbed energy …

A hybrid reconstruction method for quantitative PAT

K Ren, H Gao, H Zhao - SIAM Journal on Imaging Sciences, 2013 - SIAM
The objective of quantitative photoacoustic tomography (qPAT) is to reconstruct the diffusion
and absorption properties of a medium from data of absorbed energy distribution inside the …

Bayesian inference of the spatial distributions of material properties

A Vigliotti, G Csányi, VS Deshpande - Journal of the Mechanics and Physics …, 2018 - Elsevier
The inverse problem of estimating the spatial distributions of elastic material properties from
noisy strain measurements is ill-posed. However, it is still typically treated as an optimisation …

Lamé parameter estimation from static displacement field measurements in the framework of nonlinear inverse problems

S Hubmer, E Sherina, A Neubauer, O Scherzer - SIAM Journal on Imaging …, 2018 - SIAM
We consider a problem of quantitative static elastography, the estimation of the Lamé
parameters from internal displacement field data. This problem is formulated as a nonlinear …

When data driven reduced order modeling meets full waveform inversion

L Borcea, J Garnier, AV Mamonov, J Zimmerling - SIAM Review, 2024 - SIAM
Waveform inversion is concerned with estimating a heterogeneous medium, modeled by
variable coefficients of wave equations, using sources that emit probing signals and …

Error analysis of finite element approximations of diffusion coefficient identification for elliptic and parabolic problems

B **, Z Zhou - SIAM Journal on Numerical Analysis, 2021 - SIAM
In this work, we present a novel error analysis for recovering a spatially dependent diffusion
coefficient in an elliptic or parabolic problem. It is based on the standard regularized output …