Internship 2023: Resonances and relevant quantities for the object recognition

Duration: 4-6 months (with regular remuneration)
Level: Second year of Master degree or Engineers School (PFE).
Location: Factas team, Centre Inria d’Université Côte d’Azur (Sophia Antipolis)
Advisors: Dmitry Ponomarev (contact:, Juliette Leblond, Martine Olivi
Efficient identification of objects from electro-magnetic measurements is a task arising in various applied contexts. Shape and material properties of an object are encoded in response of the object to an incident field. The notion of resonances is intrinsic to the shape of a perfectly conducting or penetrable object. Vaguely speaking, resonances are analogs of eigenvalues in context of exterior problems. This analogy also leads to the so-called singularity expansion method (SEM), a field representation approach conceived by engineers in early 1970s. Namely, SEM can be viewed as a counterpart of the classical eigenfunction expansion method for problems on bounded domains. There are different ways to precisely define and characterise resonances.
Some of these possibilities are constructive, and hence yield viable computational strategies. The main goal of the internship is to constructively review a massive amount of literature accumulated over the last decades in this area aiming to single out the most suitable way of computing resonances from the type of data available in experimental set-ups of our partner LEAT (Laboratoire d’Electronique Antennes & Télécommunications), a CNRS lab at UCA (Université Côte d’Azur).
While functions appearing in the SEM method are relevant to the shape of the object, the coefficients of
the field expansion encode the full geometry of the scattering problem, i.e. object orientation with respect to the incident field. Study of reliable identification of these coefficients from the scattering response would be a next natural step towards an appropriate formulation of the full inverse problem of the object classification and recognition. The latter could become the subject of a follow-up Ph.D. thesis.
The proposed internship is meant to bridge a gap between the rigorous mathematical theory of resonances [1] (which has recently received a new spark of attention due to the emergence of metamaterials) and practical approaches found in engineering and physics literature [2]. The focus will be put on the computational part and pertinence of the developed methodology to the particular experimental set-up.
Since the mathematical rigour is expected to be maintained, the ideal candidate should have interests in both theoretical aspects and applications in engineering or physics.
[1] Ramm, A. G., “Mathematical foundations of the singularity and eigenmode expansion methods (SEM and EEM)”, J. Math. Anal. & Appl., 86, 562–591, 1982.
[2] Zaky, Y., “Decomposition of the scattered field into singularities for object classification using artificial intelligence algorithms”, Ph.D. thesis (Université Côte d’Azur), 2022.

About Juliette LEBLOND

Little biblio

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