Topic of the thesis :

The aim of this thesis is to develop new methods for source localization and resolution of MIMO radar, 2D planar array and distributed array systems. This method will build upon recent advances in subspace learning and low-rank matrix factorization, that have not been adapted to this application field. They notably require some new developments due to the specificity of radar data: complex-valued measurements, impulsive noise, inherent structures tied to the MIMO setup and array geometries, multi-source resolution, etc.

Methodology :

Most modern source localization methods rely on the estimation of the signal subspace. This quantity is in practice unknown and has to be recovered from a set of noisy data. In this scope, we will develop new robust signal subspace estimation in the form of optimization problems. Notably, this thesis will address current research issues related to

• the design of the objective function so that it is relevant to radar noise, MIMO radar, planar, and distributed array structure (Kronecker product, low-rank tensors). We will also leverage low-rank matrix completion formulations to deal with partially structured arrays (e.g. planar array with missing elements or antenna selection under bandwidth constraint)

• the development of efficient optimization methods to obtain the solution of the newly designed problems. We will consider the Riemannian optimization framework and some recent alternatives such as deep unfolding methods.

• the analysis of statistical performance of the newly developed methods when the solution appears as a fixed-point with tractable expression. Additionally, we will evaluate of algorithms’ performance to locate closely spaced sources and their potential ability to distinguish the target direct path from its multipath.

• the validation of Sondra experimental data for multiple sources localization and the comparison with state of art algorithms.

Supervision team contacts:

Chengfang Ren, SONDRA, CentraleSupelec, chengfang.ren@centralesupelec.fr

Mohammed Nabil El Korso, L2S, CentraleSupelec, mohammed.el-korso@universite-paris-saclay.fr

Arnaud Breloy, CEDRIC, CNAM, arnaud.breloy@lecnam.net

Philippe Forster, SATIE, ENS Paris Saclay, pforster@parisnanterre.fr

Applicants must send via e-mail to the supervision team with a CV as well as a transcript of the two previous years study.

Candidate profile

The candidate must have the equivalent of a master's degree in the field of signal and image processing, applied mathematics or remote sensing. A solid background in programming skills in Matlab or Phyton is also required. Only applicants with E.U. nationality will be considered, due to funding constraints.

Location: CentraleSupelec, SONDRA and L2S Paris-Saclay

References

• M. Muzeau, C. Ren, S. Angelliaume, M. Datcu and J. -P. Ovarlez, ”Self-Supervised Learning Based Anomaly Detection in Synthetic Aperture Radar Imaging,” in IEEE Open Journal of Signal Processing, vol. 3, pp. 440-449, 2022, doi: 10.1109/OJSP.2022.3229618.

• H. Brehier, A. Breloy, C. Ren, G. Ginolhac, ”Through the Wall Radar Imaging via Kroneckerstructured Huber-type RPCA”, Signal Processing, 2023

• J. A. Barrachina, C. Ren, C. Morisseau, G. Vieillard, J.-P. Ovarlez, ”Real- and Complex-Valued Neural Networks for SAR image segmentation through different polarimetric representations”, Image Processing (ICIP), 2022 IEEE International Conference on, Bordeaux, France, Oct. 2022.

• Alexandre Hippert Ferrer, Florent Bouchard, Ammar Mian, Titouan Vayer, Arnaud Breloy, ”Learning graphical factor models with Riemannian optimization” In Machine Learning and Knowledge Discovery in Databases, 2023

• B. M´eriaux, C. Ren, A. Breloy, M. N. El Korso and P. Forster, ”Matched and Mismatched Estimation of Kronecker Product of Linearly Structured Scatter Matrices under Elliptical Distributions”, IEEE Transactions on Signal Processing, Vol. 69, pp. 603-616

• J. A. Barrachina, C. Ren, C. Morisseau, G. Vieillard and J. -P. Ovarlez, ”Impact of PolSAR Pre-Processing and Balancing Methods on Complex-Valued Neural Networks Segmentation Tasks,” in IEEE Open Journal of Signal Processing, vol. 4, pp. 157-166, 2023, doi: 10.1109/OJSP.2023.3246391.

• A. Hippert-Ferrer, M. N. El Korso, A. Breloy, G. Ginolhac, ”Robust low-rank covariance matrix estimation with a general pattern of missing values”, Signal Processing, Volume 195, June 2022, 108460