329. Learning Total-Variation Regularization Parameters via Weak Optimal Transport
Invited abstract in session FD-7: Optimal Transport for Machine Learning and Inverse Problems, stream Optimization for Inverse Problems and Machine Learning.
Friday, 14:10 - 15:50Room: M:I
Authors (first author is the speaker)
| 1. | Enis Chenchene
|
| 2. | Kristian Bredies
|
| Institute for Mathematics and Scientific Computing, University of Graz |
Abstract
We introduce a novel method for data-driven tuning of regularization parameters in total-variation denoising. The proposed approach leverages the semi-dual Brenier formulation of weak optimal transport between the distributions of clean and noisy images to devise a new loss function for total variation parameter learning. Our loss has a close connection to the traditional bilevel quadratic setting, but it leads to fully explicit monolevel problems, which are, in fact, convex under certain conditions. For training, we introduce a new conditional-gradient-type method, which can handle a complex and unbounded constraint set with computations up to numerical precision. Numerical experiments demonstrate the effectiveness of our approach and suggest promising avenues for future extensions.
Keywords
- Optimization for learning and data analysis
- Data driven optimization
- Convex and non-smooth optimization
Status: accepted
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