Romain Petit
About
I am a postdoctoral researcher at MaLGa, in the mathematics department of the University of Genoa, working with Giovanni S. Alberti on inverse problems for PDEs. I obtained my PhD in mathematics from University Paris Dauphine, under the supervision of Vincent Duval and Yohann De Castro (I was also a member of the INRIA team MOKAPLAN).
Research interests
Inverse problems in imaging
Grid-free / off-the-grid sparse estimation
Calculus of variations
Shape optimization
Publications
[2] Exact recovery of the support of piecewise constant images via total variation regularization, with Y. De Castro and V. Duval, in preparation.
[1] Towards off-the-grid algorithms for total variation regularized inverse problems, with Y. De Castro and V. Duval.
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Exact recovery of the support of piecewise constant images via total variation regularization
with Y. De Castro and V. Duval, in preparation.
with Y. De Castro and V. Duval, in preparation.
[1] Towards off-the-grid algorithms for total variation regularized inverse problems, with Y. De Castro and V. Duval.
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Towards off-the-grid algorithms for total variation regularized inverse problems
with Y. De Castro and V. Duval, Journal of Mathematical Imaging and Vision, 2022.
with Y. De Castro and V. Duval, Journal of Mathematical Imaging and Vision, 2022.
Abstract. We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed mesh, our approach exploits the structure of the solutions and consists in iteratively constructing a linear combination of indicator functions of simple polygons.
Erratum. In the journal version of the article, Figure 2 is incorrect (the output of "Condat's total variation" is missing). The correct figure can be found in the arXiv version. We found a way to avoid the lengthy discussion in Remark 3 and Appendix B. This is explained in my thesis manuscript (Part 3, Section 1.2).
- Long version, Journal of Mathematical Imaging and Vision, 2022.
- Short version, proceedings of the 8th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), 2021.
PhD thesis
Reconstruction of piecewise constant images via total variation regularization: exact support recovery and grid-free numerical methods, defended on December 2022.
