Wavelets in the deep learning era
File(s)
Accepted version
Author(s)
Ramzi, Zaccharie
Michalewicz, Kevin
Starck, Jean-Luc
Moreau, Thomas
Ciuciu, Philippe
Type
Journal Article
Abstract
Sparsity-based methods, such as wavelets, have been the state of the art for more than 20 years for inverse problems before being overtaken by neural networks. In particular, U-nets have proven to be extremely effective. Their main ingredients are a highly nonlinear processing, a massive learning made possible by the flourishing of optimization algorithms with the power of computers (GPU) and the use of large available datasets for training. It is far from obvious to say which of these three ingredients has the biggest impact on the performance. While the many stages of nonlinearity are intrinsic to deep learning, the usage of learning with training data could also be exploited by sparsity-based approaches. The aim of our study is to push the limits of sparsity to use, similarly to U-nets, massive learning and large datasets, and then to compare the results with U-nets. We present a new network architecture, called learnlets, which conserves the properties of sparsity-based methods such as exact reconstruction and good generalization properties, while fostering the power of neural networks for learning and fast calculation. We evaluate the model on image denoising tasks. Our conclusion is that U-nets perform better than learnlets on image quality metrics in distribution, while learnlets have better generalization properties.
Date Issued
2022-11-27
Date Acceptance
2022-09-18
Citation
Journal of Mathematical Imaging and Vision, 2022
ISSN
0924-9907
Publisher
Springer
Journal / Book Title
Journal of Mathematical Imaging and Vision
Copyright Statement
© The Author(s) 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Subjects
0102 Applied Mathematics
0801 Artificial Intelligence and Image Processing
0802 Computation Theory and Mathematics
Artificial Intelligence & Image Processing
Publication Status
Published online
Date Publish Online
2022-10-27