Matteo Santacesaria

Learning sparsity-promoting regularizers for linear inverse problems This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis opera...

6/ 📄 Check out the full paper: arxiv.org/abs/2412.16031

5/ The paper extends previous work on Tikhonov regularization by tackling non-differentiable norms and developing a data-driven approach for sparse regularization in infinite dimensions.

4/ We demonstrate the approach through concrete examples including:
- Learning compact perturbations of known operators
- Learning optimal mother wavelets

3/ Our framework comes with theoretical guarantees - we establish well-posedness of the optimization problem and provide sample complexity bounds, bridging theory and practice.

2/ Key idea: Instead of using fixed regularizers, we learn an optimal synthesis operator B that promotes sparsity in a way that's tailored to your specific inverse problem and noise model.

1/ We develop a novel bilevel optimization framework to learn sparsity-promoting regularizers that adapt to your data, while incorporating prior knowledge about the structure of solutions.

🧵 Excited to share our new preprint on learning optimal regularizers for inverse problems! With GSAlberti, EDeVito, THelin, MLassas, LRatti