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 …
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
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 …
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
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 …
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 …
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 …
thermodynamic properties of heterogeneous media from data of absorbed energy …
A hybrid reconstruction method for quantitative PAT
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 …
and absorption properties of a medium from data of absorbed energy distribution inside the …
Bayesian inference of the spatial distributions of material properties
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 …
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
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 …
parameters from internal displacement field data. This problem is formulated as a nonlinear …
When data driven reduced order modeling meets full waveform inversion
Waveform inversion is concerned with estimating a heterogeneous medium, modeled by
variable coefficients of wave equations, using sources that emit probing signals and …
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
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 …
coefficient in an elliptic or parabolic problem. It is based on the standard regularized output …