The Inverse Problems Group (GPI, Groupe Problèmes Inverses) stands at
the interface between physics and signal and image processing.
Research topics are connected to the capture and reconstruction of signals and images, based on physical modeling and bayesian and variational methods. Main applications include analysis of audio recordings, non-destructive testing and analysis of massive astrophysical data.
Classical sparsity models can be enriched by additional constraints, such as support constraints (e.g. nonzero coefficients appearing as blocks) or positivity constraints. These models lead to the development of new estimation algorithms, such as positive greedy algorithms, or new thresholding schemes.
Quantification of the uncertainties of these approaches is an ongoing research topic.
Non-parametric bayesian methods for inverse problems (tomography, image restoration, etc.) are subject to the curse of dimensionality. Bayesian methods for high-dimensional setting are developed by the GPI, based on new sampling methods or bayesian variational approximations.
Image restoration is an important part of modern imaging techniques, in particular in microscopy. Structured illumation techniques and associated reconstruction methods are developed by the group, allowing
fast imaging of biological samples with improved image resolution.
The complexity of estimation algorithms and the scale of the
data are constantly rising. The adequation between algorithms and computer architectures allows to tackle such challenging problems. The group is in particular involved in GPU and FGPA architectures, applied in tomography, and high performance processing of radio astronomy signals of the Square Kilometer Array.