On statistical Calderón problems

K Abraham, R Nickl - Mathematical Statistics and Learning, 2020 - ems.press
For D a bounded domain in Rd; d 2; with smooth boundary@ D, the non-linear inverse
problem of recovering the unknown conductivity determining solutions u D u; f of the partial …

Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches

DN Tanyu, J Ning, A Hauptmann, B Jin… - arXiv preprint arXiv …, 2023 - arxiv.org
Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse
applications, eg, medical diagnosis, industrial monitoring, and environmental studies. The …

Non-convex ℓp regularization for sparse reconstruction of electrical impedance tomography

J Wang - Inverse Problems in Science and Engineering, 2021 - Taylor & Francis
This work is to investigate the image reconstruction of electrical impedance tomography from
the electrical measurements made on an object's surface. An ℓ p-norm (0< p< 1) sparsity …

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

B Jin, 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 …

Reduction of staircase effect with total generalized variation regularization for electrical impedance tomography

Y Shi, X Zhang, Z Rao, M Wang… - IEEE Sensors …, 2019 - ieeexplore.ieee.org
Image reconstruction in electrical impedance tomography is an ill-posed inverse problem.
To address this problem, regularization methods such as Tikhonov regularization and total …

Acousto-electric tomography with total variation regularization

BJ Adesokan, B Jensen, B Jin, K Knudsen - Inverse problems, 2019 - iopscience.iop.org
We study the numerical reconstruction problem in acousto-electric tomography of recovering
the conductivity distribution in a bounded domain from interior power density data. We …

A non-convex regularization method combined with Landweber method for image reconstruction in electrical resistance tomography

Y Shi, Q Li, M Wang, W Liu, Z Tian - Flow Measurement and Instrumentation, 2021 - Elsevier
Electrical resistance tomography (ERT) is a promising technique with which the conductivity
distribution in the detected region can be visualized. Mathematically, the reconstruction of …

Compressive sensing ghost imaging based on image gradient

C Yi, C Zhengdong, F Xiang, C Yubao, L Zhenyu - Optik, 2019 - Elsevier
In order to improve the imaging quality of ghost imaging and solve the problem of high
distortion at a low sampling rate, the compressive sensing ghost imaging based on image …

Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity

B Jin, Y Xu - Inverse Problems, 2019 - iopscience.iop.org
In this work we propose and analyze a numerical method for electrical impedance
tomography to recover a piecewise constant conductivity from boundary voltage …

Application of a class of iterative algorithms and their accelerations to Jacobian-based linearized EIT image reconstruction

J Wang, B Han - Inverse Problems in Science and Engineering, 2021 - Taylor & Francis
This work is concerned with the image reconstruction of the Jacobian-based linearized EIT
problem. Based on the homotopy perturbation technology, we first propose a novel class of …