PhD Position F/M Construction of a simulation-ready torso conductivity map library and data generation for the electrical impedance tomography (EIT) Bayesian inverse problem

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Type de contrat : CDD

Niveau de diplôme exigé : Bac + 5 ou équivalent

Autre diplôme apprécié : Master's degree in Applied Mathematics

Fonction : Doctorant

A propos du centre ou de la direction fonctionnelle

The Inria Saclay-Île-de-France Research Centre was established in 2008. It has developed as part of the Saclay site in partnership with Paris-Saclay University and with the Institut Polytechnique de Paris .

The centre has 39 project teams , 27 of which operate jointly with Paris-Saclay University and the Institut Polytechnique de Paris; Its activities occupy over 600 people, scientists and research and innovation support staff, including 44 different nationalities.

Contexte et atouts du poste

This PhD project is a part of a new collaboration between Idefix Team (Inria Saclay) and Carmen Team (Inria
Bordeaux).

The project is financed by Inria program Action Exploratoire REALPRIOREIT. The co-PI of the project is Lisl Weynans of Equipe Carmen, Inria Bordeaux.

The PhD student will be based in the Idefix Team, Inria-Saclay, located at ENSTA Paris, Unité de Mathématiques Appliquées (UMA) 828, Boulevard des Maréchaux, 91762 Palaiseau, France.

There will be some travel between Saclay and Bordeaux. There will be regular meetings by video-conference with supervisers. Shared code development will be on GitHub.

 

Mission confiée

In this project, we study the reconstruction capabilities of Bayesian inference methods for biomedical inverse problems. The primary application is electrical impedance tomography (EIT). In particular, we plan to construct statistical distributions of realistic human torso volume geometries and incorporate them in Bayesian inference methods for the EIT inverse problem. This a priori information will be obtained from publicly available CT and MRI images as well as artificially generated images from training images.

Our starting point will be publicly available CT images in two repositories. The CT images will be used to construct a library of realistic conductivity maps that serve as inputs to the forward solver of the EIT problem. The forward solver will be an immersed boundary method to which the pixelated conductivity maps can be coupled in a natural way. A large number of numerical simulations will beperformed to generate EIT data under a variety of experimental conditions for the conductivity maps in the library.

The constructed data libraries will be used to provide prior distribution information on the conductivity maps to be estimated in the EIT torso inverse problem. We will also provide statistical distributions of biological and geometrical parameters associated with the conductivity maps in the library. We expect to incorporate the libraries and the statistical information in a Bayesian inversion algorithm.

The methodology will be developed in two dimensions and extended to three dimensions using HPC tools. Both the conductivity maplibrary and the simulated EIT data library will be made publicly available.

Principales activités

Use software from medical imaging to perform automatic segmentation;

Compute statistical information about the segmented organs;

Couple pixelated conductivity maps to the EIT forward solver, analyze sensitivity;

Work with collaborators in Bordeaux to constructe data libraries to provide prior distribution information for the EIT torso inverse problem. 

Code in Python and Matlab;

Write up results in Latex;

Compétences

Master diploma in Applied Mathematics; Course work in partial differential equations and their numerical discretization, statistics and machine learning. Coding in Matlab and Python;

Avantages

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage

Rémunération

Monthly gross salary : 2.200 euros/month