Theoretical Guarantees in Inverse Problems: From Self-Supervised Networks to Blind Tikhonov Regularization
| When |
Sep 23, 2025
from 01:00 to 02:00 |
|---|---|
| Where | M7 101 |
| Attendees |
Nathan Buskulic |
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Nathan Buskulic
Title: Theoretical Guarantees in Inverse Problems: From Self-Supervised Networks to Blind Tikhonov Regularization
While neural networks have proven to be very powerful tools for the resolution of inverse problems, even in the self-supervised case, they lack strong theoretical guarantees, especially recovery ones. In the first part of this talk, I will provide convergence and recovery guarantees for self-supervised neural networks applied to inverse problems when trained with various algorithms, including first- and second-order methods. I will also show some experimental results using Deep Inverse Prior on imaging inverse problems demonstrating the advantages of using second-order methods when the optimization parameters are chosen properly.
I will then turn to the more challenging setting of blind inverse problems, where the exact forward operator is unknown. There I will discuss variational approaches that incorporate a learned regularizer. I will show that under an adapted source condition, the optimal Tikhonov regularizer one can learn leads to new error bounds that generalize the previously known ones in the non-blind setting.
Website: https://nathanbuskulic.github.io/
In Room M7 101, 1st floor, Monod campus, ENSL.