The Inverse Problems and Imaging theme lies at the interface of physics, statistical signal and image processing, and statistical learning. It develops reconstruction methods from indirect data using physical models and variational, Bayesian, and learning-based inversion approaches.

Research directions include:

learning-based inversion and the integration of physical constraints into AI models,
new methods for multichannel inverse problems,
optimal transport for regularizing multivariate inverse problems,
the enhancement of classical inversion techniques with statistical learning tools,
Bayesian and generative approaches to uncertainty quantification.

The objective is to design robust, interpretable methods for complex data that are often large-scale, noisy, or incomplete. Applications include non-destructive testing, biomedical imaging, hyperspectral imaging in astrophysics, and acoustic and radar source localization.

This methodological and application-driven research is supported by major collaborative projects such as Dark-Era and PEPR Origins, national partners including GeePs, SATIE, CEA List, SONDRA, LS2N, I2M, and Institut d’Alembert, international collaborations, and industrial partners including Safran, Thales, Eviden/Bull, and Forvia.

Learning-based inversion: AI and physics

Machine learning methods open new perspectives for solving inverse problems, through a close integration with physical modeling. The research aims to incorporate unrolling architectures, plug-and-play methods, and deep equilibrium models into physics-constrained inversion frameworks. The challenge is to reconcile numerical performance, interpretability, and compliance with the laws governing the forward model. Particular attention is devoted to the theoretical analysis (stability, convergence, robustness) of these hybrid approaches. These developments find applications in imaging and signal processing in highly nonlinear or noisy contexts.

Source localization

Source localization and characterization from sensor networks pose major challenges when acoustic or electromagnetic sources are multiple, correlated, or observed under imperfect acquisition conditions. The research focuses on the development of methods adapted to complex configurations (correlated and extended sources, asynchronous sensor networks) and high-dimensional settings. Particular attention is devoted to gridless approaches and sparse methods. The research also includes contributions to the theoretical analysis of performance limits, as well as to the design of acquisition systems. These developments aim to improve the accuracy and robustness of source localization methods.

Biomedical imaging

Physical imaging for life sciences relies on accurate physical models and advanced inversion techniques. The research focuses on physics-guided approaches (Bayesian, tomographic, deep learning-based, etc.) to solve nonlinear and ill-posed inverse problems.

The research particularly addresses the exploitation of multi-/hyperspectral data and multimodal data fusion, with applications in biomedical imaging (breast, brain) combining microwaves, ultrasound, or electrical impedance tomography. The developed methods aim to improve the resolution, contrast, and quantitative characterization of internal structures, while leveraging data acquired from innovative experimental devices. These methods also find applications in other fields of physical and computational imaging, particularly in non-destructive testing.

Bayesian approaches and diffusion models

This research develops Bayesian approaches for inverse problems, enabling rigorous uncertainty quantification. The work relies on advanced probabilistic models, including variational methods and recent generative models such as diffusion processes. The objective is to estimate posterior distributions rather than point estimates, while incorporating complex prior information. These approaches provide a coherent framework for handling incomplete or highly noisy data. They are applied in imaging, astrophysics, and high-dimensional data analysis.

Computational hyperspectral imaging and astrophysics

Hyperspectral data provide rich access to spectral and spatial information, but their exploitation requires addressing major challenges in reconstruction, data fusion, and source separation. The research focuses on the analysis and reconstruction of hyperspectral imaging data, particularly in astrophysics. The work addresses heterogeneous data fusion, source unmixing, and the modeling of instrumental degradations. The developed approaches rely on advanced optimization methods combined with appropriate physical models. Particular attention is paid to the management of massive datasets and to computational efficiency. This research is conducted within the framework of collaborations involving large-scale international projects.

Non-destructive testing

Wave propagation inverse problems (electromagnetic, from quasi-static to THz frequencies, ultrasonic, thermal, etc.) provide access to information about the structure and properties of complex media. The research combines detailed physical modeling with the development of inversion methods adapted to realistic scenarios (partial data, noise, uncertainties). Particular attention is devoted to fast and robust methods, as well as to the consideration of non-ideal acquisition conditions. The applications particularly target the detection and characterization of defects in industrial structures. This research axis is supported by a strong network of academic and industrial collaborations.