Research themes
- Harmonic analysis and design of microwave devices.
Factas is concerned with the development of formalism, methods and algorithms to help fully automated, or at least computer assisted, design and tuning of microwave components such as filters, multiplexers, amplifiers and oscillators. Its contributions fall in two classes.
The first one concerns design problems where the “best” transfer function in the sense for example of power transfer or selectivity is sought. The optimisation procedure is typically carried out over a functional class restricted by realisability constraints, passivity constraints, or topological constraints on the circuit induced by electrical considerations weighing the final implementation of the device.
The second class of problems is system identification which is used by the team to design tools for diagnosis of microwave hardware from input/output frequency data, obtained through measurements or full-wave simulations. The objective here is either to extract a circuital model, whose analysis allows one to infer dimensional modifications to be made on the hardware, or else a stability/instability assessment in the case of active systems. - Inverse potential problems.
A prototypical inverse potential problems is to estimate the location and 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 EEG/MEG data, to locate electric activity in the brain or to estimate the conductivity of tissues;
(ii) paleomagnetism, where magnetization distributions in rock samples are to be reconstructed in order to get information on their past history, or geomagnetism where the crustal and core fields of the Earth must be determined to understand the evolution of the geodynamo.
These are ill-posed problems that suffer non-uniqueness and instability issues which are studied by Factas. Two main different regularising approaches are proposed, the first one deals with a discrete model for the source term, the second one makes a measure-theoretic assumption on the support of the sources that serves as a notion of sparsity in this context. Recovery algorithms are developed in the team, together with appropriate approximation techniques, and software tools.
