Ongoing project consists in investigating a new approach to extend the off-the-grid theory (right now limited to points) to the reconstruction of more exotic structures like curves, from both theoretical and numerical standpoints. Through the definition of new operator and variational problem, we worked on the localisation of spikes with time-dependent amplitude (and static position), a proxy of the discrete COL0RME model. we developed a new gridless method in a dynamical context.we implemented several algorithms for off-the-grid methods taken from the literature in a efficient and user-friendly Python module.We develop new gridless methods in static or dynamic settings, with applications to biomedical imaging. In this context appropriate energy functionals are defined typically enforcing sparsity by means of Total Variation minimisation. as elements of the Banach space of Radon measures. Instead of standard discrete modelling where molecules are described as image pixels on a coarse (low-resolution) and fine (high-resolution) grid, off-the-grid variational methods models molecules as weighted sum of Dirac masses, i.e. Publications: ICASSP 2022, preprint HAL. Participants: Bastien Laville, Laure Blanc-Féraud, Gilles Aubert. Off-the-grid dynamic super-resolution for fluorescence microscopy (Left upper part) super-resolved 3D-COL0RME image, (right lower part) standard MA-TIRF reconstruction. The proposed methods has been validated on simulated MA-TIRF blinking-type data and on challenging realMA-TIRF acquisitions, showing significant resolution improvements. Differently from state-of-the-art approaches, 3D-COL0RME does not require the use of special equipment as it can be used with standard fluorophores. Our approach, called 3D-COL0RME improves both lateral and axial resolution by combining sparsity-based modelling for precise molecule localisation and intensity estimation in the lateral plane with a 3D reconstruction procedure in the axial one usingMulti-Angle TIRF (MA-TIRF). We also proposed a 3D super-resolution approach to improve spatial resolution in Total Internal Reflectance Fluorescence (TIRF) imaging applications. Our results show that COL0RME outperforms competing methods exploiting analogously temporal fluctuations in particular, it achieves better localization, reduces background artifacts and avoids fine parameter tuning. Several numerical results both on synthetic and real fluorescent microscopy images and several comparisons with state-of-the art approaches have been done. Based on this idea, we proposed COL0RME, a method for COvariancebased $\ell_0$ super-ResolutionMicroscopy with intensity Estimation, which achieves good spatio-temporal resolution by solving a sparse optimization problem in the covariance domain, discuss automatic parameter selection strategies, estimates background and noise statistics and includes a final estimation step where intensity information is retrieved. Analyzing the stochastic fluctuations of the fluorescentmolecules provides a solution to the aforementioned limitations. However, state-of-the-art approaches require specific and often demanding acquisition conditions to achieve adequate levels of both spatial and temporal resolution.
Super-resolution light microscopy overcomes the physical barriers due to light diffraction. Publications: ISBI2021, Biological Imaging, ISBI2022 Participants: Vasiliki Stergiopoulou, Luca Calatroni, Laure Blanc-Féraud, Sebastien Schaub, Henrique Goulart. 2D and 3D covariance-based $\ell_0$ super-Resolution Microscopy with intensity Estimation (COL0RME) Here you can find a list of our recent and ongoing projects.
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