Starting date: october 2026
Level: Master 2 or equivalent
Salary: according to regulation (about. 2200€ gross/month)
Localization: IRIMAS laboratory in Mulhouse, France
Application deadline: 09 April 2026
Off-the-grid sparsity tools are optimization methods in measure spaces that have seen significant fundamental and algorithmic developments over the past 15 years. In particular, they allow for the explicit formulation of reconstruction conditions in an inverse problem with sparsity constraints, and for the development of algorithms that utilize these conditions [1].
This thesis offer studies the problem in the context of observing multicomponent signals via time-frequency (TF) transforms [2]. These families of methods allow for a richer representation of temporal signals, but nevertheless suffer from intrinsic limitations: uncertainty in time/frequency localization, and an increase in the representation dimension. The objective is therefore to be able to locate, identify, and separate the different components of a single signal based on its TF representation.
This work falls within the broader framework of off-the-grid curve sparsity [3], with TF transforms as the primary representation (generalizing the work in [4] and [5] in particular). The goal is to develop a comprehensive methodology: mathematical methods, algorithms, and applications on real-world data. Regarding the latter, we plan to work on the classification of lung sounds already acquired as part of a collaboration with physicians.
Qualifications
- Master’s degree or equivalent.
- Strong background in applied mathematics or signal and image processing. Training or experience in optimization in measure spaces or time-frequency transforms would be particularly welcome.
- Good programming skills, particularly in Python or MATLAB.
- Proficiency in English.
Team
This thesis will be conducted within the IMTIS team (multimodal imaging, image and signal processing) at the IRIMAS laboratory in Mulhouse. It will be supervised by Jean-Baptiste Courbot and Ali Moukadem, and co-supervised by Bruno Colicchio and Alain Dieterlen at IRIMAS and Kévin Polisano at the LJK (Jean Kuntzmann Laboratory, Grenoble) as part of a collaboration between IRIMAS, the LJK, and ENS Lyon.
Application
To apply, please send a CV, a cover letter, as well as the recent academic records before the 9th April 2026 at : jean-baptiste.courbot@uha.fr ali.moukadem@uha.fr
References
[1] Denoyelle et al. (2019). The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy. Inverse Problems,
[2] Miramont et al. Benchmarks of multi-component signal analysis methods. 2023 31st European Signal Processing Conference (EUSIPCO). IEEE, 2023.
[3] Laville et al. (2024). A Γ-convergence result and an off-the-grid charge algorithm for curve reconstruction in inverse problems. Journal of Mathematical Imaging and Vision.
[4] Khodaverdi et al. (2025). A greedy algorithm for the estimation of instantaneous frequencies in the time-frequency plane. In XXXe Colloque Francophone de Traitement du Signal et des Images (Gretsi 2025)
[5] Polisano et al. (2024). Gridless 2D recovery of lines using the Sliding Frank-Wolfe algorithm. In 2024 32nd European Signal Processing Conference (EUSIPCO).
