Hi! I’m an Assistant Professor of Applied Mathematics at Loyola University Andalusia. When I’m not immersed in numerically solving mathematical models, I enjoy capturing the world through photography, discovering new places and making friends while traveling.
Bio
Interests
- Bilevel Optimization
- Data Science & Machine Learning
- Mathematical Image Processing
Formation
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PhD in Applied Mathematics, 2022Escuela Politécnica Nacional - Ecuador
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MSc in Computer Science, 2014University of Birmingham - UK
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Electronics Engineering, 2012Escuela Politécnica Nacional - Ecuador
Recent Publications
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De los Reyes, Juan Carlos, Villacís, David
Interpretable model learning in variational imaging: a bilevel optimization approach
IMA Journal of Applied Mathematics, volume 89, number 1, pages 85-122, September 2023, doi: 10.1093/imamat/hxad024
In this paper, we investigate the use of bilevel optimization for model learning in variational imaging problems. Bilevel learning is an alternative approach to deep learning methods, which leads to fully interpretable models. However, it requires a …
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De los Reyes, Juan Carlos, Villacís, David
Optimality conditions for bilevel imaging learning problems with total variation regularization
SIAM Journal on Imaging Sciences, volume 15, number 4, pages 1646-1689, December 2022, doi: 10.1137/21M143412X
We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For the bileve…
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