Are the Methods of Convex Analysis Competitive with Deep Neural Networks?
M. Unser
Keynote address, Machine Learning Research, Second Conference on Parsimony and Learning (CPAL'25), Stanford CA, USA, March 24-27, 2025.
Computational imaging is currently dominated by two paradigms. Traditional variational methods, supported by well-established theory, provide guarantees for convergence, stability, and signal recovery from limited measurements, as in compressed sensing. In contrast, deep neural network methods generally achieve superior image reconstruction but suffer from a lack of robustness (tendency to hallucinate) and theoretical understanding. This raises a fundamental question: Can variational methods be improved by learning the regularizer while maintaining their theoretical guarantees? To address this, we introduce a general framework for image reconstruction under the constraints of amplitude-equivariance and convexity. We demonstrate that polyhedral norms enable universality, allowing for the design of trainable regularization architectures. These architectures outperform traditional sparsity-based methods, and help us bridge the gap between theoretical rigor and practical performance in computational imaging.
@INPROCEEDINGS(http://bigwww.epfl.ch/publications/unser2502.html,
AUTHOR="Unser, M.",
TITLE="Are the Methods of Convex Analysis Competitive with Deep Neural
Networks?",
BOOKTITLE="Machine Learning Research, Second Conference on Parsimony and
Learning ({CPAL'25})",
YEAR="2025",
editor="",
volume="",
series="",
pages="",
address="Stanford CA, USA",
month="March 24-27,",
organization="",
publisher="",
note="Keynote address")