Research themes
Inverse problems
- Inverse potential problems
Such problems consist in estimation of the location and the strength of a collection of sources from measurements of the potential or of the field they generate. Two application fields are specifically targeted:
(i) Brain imaging, with the processing of electro-/magneto-encephalography (EEG/MEG) datasets, to locate electric activity in the brain.
(ii) Paleomagnetism, where magnetisation distributions in ancient planetary rock samples are to be reconstructed from measurements of the generated magnetic field, in order to get information on their past history. Another variants of this problem such as net magnetic moment estimation and data extension problems are also studied. They are physically meaningful issues on their own rights, but also helpful for the full magnetisation reconstruction. - Inverse scattering issues
In this context, we deal with shape identification and reconstruction of electrical characteristics of a scatterer. As opposed to classical electromagnetic imaging where several spatially located sensors are used to identify the object by means of measured data at a single frequency, a discrimination process between different metallic objects is here being sought for by means of a single, or a reduced number of sensors that operate on a whole frequency band.
The behaviour of underlying quantities (electric potential, electromagnetic fields) is modeled by Maxwell equations, thereby by Poisson or Helmholtz partial differential equations (PDE) in the above frameworks. These are ill-posed problems that suffer non-uniqueness and instability issues which are studied by Factas, employing different regularisation approaches.
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- Inverse problems in hip prosthetic surgery
In this recent application domain, stability of the implant should be determined by estimating bone and contact parameters, thanks to measurements taken by a sensor attached to a press-fit hammer. Here, several coupled nonlinear problems have to be solved since regions corresponding to the bone, the implant and the hammer all possess different material properties.
Harmonic analysis and design of microwave devices
Factas used to be concerned with the formalism, methods and algorithms to help design and tuning of microwave components such as filters, multiplexers, amplifiers and oscillators. Its contributions were mostly related to system identification in order to derive tools for diagnosis of microwave hardware from input/output frequency data, obtained through measurements or full-wave simulations. Dedicated software tools have been developed. An objective of the team remains to infer stability/instability assessment in the case of active systems.
Activity report
You will find our 2024 activity report here.
