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The winner of the 2018 French-German Mathematics in Imaging PhD Prize is
Emmanuel Soubies (EPFL, Lausanne)
for his PhD thesis
On some reconstruction problems in MA-TIRF imaging and sparse optimization using continuous exact relaxation of $\ell_0$-penalized criteria
Short abstract of PhD thesis: This thesis is devoted to two problems encountered in signal and image processing. The first one concerns the 3D reconstruction of biological structures from multi-angle total interval reflection fluorescence microscopy (MA-TIRF). Within this context, we propose to tackle the inverse problem by using a variational approach and we analyze the effect of the regularization. A set of simple experiments is then proposed to both calibrate the system and validate the used model. The proposed method has been shown to be able to reconstruct precisely a phantom sample of known geometry on a 400 nm depth layer, to co-localize two fluorescent molecules used to mark the same biological structures and also to observe known biological phenomena, everything with an axial resolution of 20 nm. The second part of this thesis considers more precisely the $\ell_0$ regularization and the minimization of the penalized least squares criteria ($\ell_2$-$\ell_0$) within the context of exact continuous relaxations of this functional. Firstly, we propose the Continuous Exact $\ell_0$ (CEL0) penalty leading to a relaxation of the $\ell_2$-$\ell_0$ functional which preserves its global minimizers and for which from each local minimizer we can define a local minimizer of $\ell_2$-$\ell_0$ by a simple thresholding. Moreover, we show that this relaxed functional eliminates some local minimizers of the initial functional. The minimization of this functional with nonsmooth nonconvex algorithms is then used on various applications showing the interest of minimizing the relaxation in contrast to a direct minimization of the $\ell_2$-$\ell_0$ criteria. Finally we propose a unified view of continuous penalties of the literature within this exact problem reformulation framework.
Download an extended abstract
Short bio: Emmanuel Soubies graduated from the Institut National des Sciences
Appliquées of Toulouse and received the M.Sc. degree in operational research from the University of Toulouse in 2013. He earned the PhD degree from the University of Nice Sophia Antipolis (UNSA) in 2016. His thesis work has been supervised by Laure Blanc-Féraud, Gilles Aubert, and Sébastien Schaub within the Morpheme team (CNRS, INRIA, UNSA). Since 2016, he is a Post-Doctoral Fellow with the Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, Switzerland. His main research interests are inverse problems for imaging and sparse optimization.
The 2018 PhD Prize jury consisted of:
Alfred Bruckstein (Technion, Haifa)
Raymond Chan (Chinese University of Hong Kong)
Selim Esedoglu (University of Michigan)
Rebecca Willett (University of Wisconsin)
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